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text:
For Identity Federations
Identity federations can join eduGAIN service as a member. If an identity federation meets the requirements for joining eduGAIN, it can initiate the joining process described in Section 3.2 of the eduGAIN Constitution.
The process to join eduGAIN is as follows:
To apply for membership, the applicant federation signs the eduGAIN Policy Declaration and presents it to the eduGAIN Operations Team (OT).
The OT confirms that the applicant federation fulfils the requirements in Section 3.1 of the eduGAIN Constitution.
Unless the eduGAIN Steering Group (eSG) has decided that the applicant federation does not need further approvals, the OT prepares and presents a proposal to the eSG to approve or reject the application.
When an applicant is approved, the OT takes the necessary technical steps to register the federation to eduGAIN.
Besides the points mentioned in that section, a more technical description of what information has to be sent to the eduGAIN operations team in order to join eduGAIN is listed on the eduGAIN Technical website and best practices are described on the eduGAIN wiki.
Joining eduGAIN means joining an eduGAIN member federation. But which one to join? There is no strict rule, but one reasonable option should be to contact the national federation of the country where the your organisation is located or where the service is geographically operated.
How to offer a service in eduGAIN provides a general overview about the aspects relevant for adding a service to eduGAIN. This is a good preparation for the following guide, which goes more into more detail.
How to join eduGAIN as Service Provider includes more concrete step-by-step instructions on what has to be done to legally and technically add a service to eduGAIN.
If you are interested to see which services are already eduGAIN-enabled, have a look at the eduGAIN Services page.
For Identity Providers
Joining eduGAIN means joining an eduGAIN member federation. You should contact the national federation of the country where the your organisation is located and check the rules and procedures for joining.
How to set up an Identity Provider for eduGAIN provides guides about various aspects relevant for adding an identity provider to eduGAIN.
Different supporting tools for identity and service providers are available at the eduGAIN technical site under the Tools section.
For users, eduGAIN couldn't be simpler. When you want to log into a service, you should click on 'login' and then select your institution from the list from all the institutions that have been granted access to the service. Sometimes, services will label this as a "Federated Login".
Once you have selected your institution, you'll be shown the standard login page from your organisation. This means that your username and password are NOT being shared with the service provider.
You might also be asked by your institution to approve the sharing of your details with the service provider. This page would list the attributes being shared (usually name and email address) so that you can be certain what information about you is being requested.
After this, you'll be logged in to the service provider.

redpajama_set_name: RedPajamaCommonCrawl


WHEN I AWOKE IN THE morning, long bands of sunshine were coming in at the window and reaching back under the eaves where the two boys lay. Leo was wide awake and was tickling his brother's leg with a dried cone-flower he had pulled out of the hay. Ambrosch kicked at him and turned over. I closed my eyes and pretended to be asleep. Leo lay on his back, elevated one foot, and began exercising his toes. He picked up dried flowers with his toes and brandished them in the belt of sunlight. After he had amused himself thus for some time, he rose on one elbow and began to look at me, cautiously, then critically, blinking his eyes in the light. His expression was droll; it dismissed me lightly. `This old fellow is no different from other people. He doesn't know my secret.' He seemed conscious of possessing a keener power of enjoyment than other people; his quick recognitions made him frantically impatient of deliberate judgments. He always knew what he wanted without thinking.
After dressing in the hay, I washed my face in cold water at the windmill. Breakfast was ready when I entered the kitchen, and Yulka was baking griddle-cakes. The three older boys set off for the fields early. Leo and Yulka were to drive to town to meet their father, who would return from Wilber on the noon train.
`I didn't even know Martha wasn't my full sister until after she was engaged to Joe,' Anna told me.
Toward the middle of the afternoon, the wagon drove in, with the father and the eldest son. I was smoking in the orchard, and as I went out to meet them, Antonia came running down from the house and hugged the two men as if they had been away for months.
`Papa,' interested me, from my first glimpse of him. He was shorter than his older sons; a crumpled little man, with run-over boot-heels, and he carried one shoulder higher than the other. But he moved very quickly, and there was an air of jaunty liveliness about him. He had a strong, ruddy colour, thick black hair, a little grizzled, a curly moustache, and red lips. His smile showed the strong teeth of which his wife was so proud, and as he saw me his lively, quizzical eyes told me that he knew all about me. He looked like a humorous philosopher who had hitched up one shoulder under the burdens of life, and gone on his way having a good time when he could. He advanced to meet me and gave me a hard hand, burned red on the back and heavily coated with hair. He wore his Sunday clothes, very thick and hot for the weather, an unstarched white shirt, and a blue necktie with big white dots, like a little boy's, tied in a flowing bow. Cuzak began at once to talk about his holiday--from politeness he spoke in English.
Cuzak nodded. `And very many send word to you, Antonia. You will excuse'--turning to me--`if I tell her.' While we walked toward the house he related incidents and delivered messages in the tongue he spoke fluently, and I dropped a little behind, curious to know what their relations had become--or remained. The two seemed to be on terms of easy friendliness, touched with humour. Clearly, she was the impulse, and he the corrective. As they went up the hill he kept glancing at her sidewise, to see whether she got his point, or how she received it. I noticed later that he always looked at people sidewise, as a work-horse does at its yokemate. Even when he sat opposite me in the kitchen, talking, he would turn his head a little toward the clock or the stove and look at me from the side, but with frankness and good nature. This trick did not suggest duplicity or secretiveness, but merely long habit, as with the horse.
He had brought a tintype of himself and Rudolph for Antonia's collection, and several paper bags of candy for the children. He looked a little disappointed when his wife showed him a big box of candy I had got in Denver--she hadn't let the children touch it the night before. He put his candy away in the cupboard, `for when she rains,' and glanced at the box, chuckling. `I guess you must have hear about how my family ain't so small,' he said.
Cuzak had brought home with him a roll of illustrated Bohemian papers. He opened them and began to tell his wife the news, much of which seemed to relate to one person. I heard the name Vasakova, Vasakova, repeated several times with lively interest, and presently I asked him whether he were talking about the singer, Maria Vasak.
When the boys came in from milking and feeding, the long table was laid, and two brown geese, stuffed with apples, were put down sizzling before Antonia. She began to carve, and Rudolph, who sat next his mother, started the plates on their way. When everybody was served, he looked across the table at me.
No, I had heard nothing at all about them.
`Hurrah! The murder!' the children murmured, looking pleased and interested.
Rudolph told his story in great detail, with occasional promptings from his mother or father.
Wick Cutter and his wife had gone on living in the house that Antonia and I knew so well, and in the way we knew so well. They grew to be very old people. He shrivelled up, Antonia said, until he looked like a little old yellow monkey, for his beard and his fringe of hair never changed colour. Mrs. Cutter remained flushed and wild-eyed as we had known her, but as the years passed she became afflicted with a shaking palsy which made her nervous nod continuous instead of occasional. Her hands were so uncertain that she could no longer disfigure china, poor woman! As the couple grew older, they quarrelled more and more often about the ultimate disposition of their `property.' A new law was passed in the state, securing the surviving wife a third of her husband's estate under all conditions. Cutter was tormented by the fear that Mrs. Cutter would live longer than he, and that eventually her `people,' whom he had always hated so violently, would inherit. Their quarrels on this subject passed the boundary of the close-growing cedars, and were heard in the street by whoever wished to loiter and listen.
Cutter went out behind the hardware store, put up a target, practised for an hour or so, and then went home. At six o'clock that evening, when several men were passing the Cutter house on their way home to supper, they heard a pistol shot. They paused and were looking doubtfully at one another, when another shot came crashing through an upstairs window. They ran into the house and found Wick Cutter lying on a sofa in his upstairs bedroom, with his throat torn open, bleeding on a roll of sheets he had placed beside his head.
One of the neighbours telephoned for a doctor, while the others went into Mrs. Cutter's room. She was lying on her bed, in her night-gown and wrapper, shot through the heart. Her husband must have come in while she was taking her afternoon nap and shot her, holding the revolver near her breast. Her night-gown was burned from the powder.
On his desk the coroner found a letter, dated at five o'clock that afternoon. It stated that he had just shot his wife; that any will she might secretly have made would be invalid, as he survived her. He meant to shoot himself at six o'clock and would, if he had strength, fire a shot through the window in the hope that passersby might come in and see him `before life was extinct,' as he wrote.
`Did you ever hear of anybody else that killed himself for spite, Mr. Burden?' asked Rudolph.
I admitted that I hadn't. Every lawyer learns over and over how strong a motive hate can be, but in my collection of legal anecdotes I had nothing to match this one. When I asked how much the estate amounted to, Rudolph said it was a little over a hundred thousand dollars.
Cuzak gave me a twinkling, sidelong glance. `The lawyers, they got a good deal of it, sure,' he said merrily.
A hundred thousand dollars; so that was the fortune that had been scraped together by such hard dealing, and that Cutter himself had died for in the end!
After supper Cuzak and I took a stroll in the orchard and sat down by the windmill to smoke. He told me his story as if it were my business to know it.
His father was a shoemaker, his uncle a furrier, and he, being a younger son, was apprenticed to the latter's trade. You never got anywhere working for your relatives, he said, so when he was a journeyman he went to Vienna and worked in a big fur shop, earning good money. But a young fellow who liked a good time didn't save anything in Vienna; there were too many pleasant ways of spending every night what he'd made in the day. After three years there, he came to New York. He was badly advised and went to work on furs during a strike, when the factories were offering big wages. The strikers won, and Cuzak was blacklisted. As he had a few hundred dollars ahead, he decided to go to Florida and raise oranges. He had always thought he would like to raise oranges! The second year a hard frost killed his young grove, and he fell ill with malaria. He came to Nebraska to visit his cousin, Anton Jelinek, and to look about. When he began to look about, he saw Antonia, and she was exactly the kind of girl he had always been hunting for. They were married at once, though he had to borrow money from his cousin to buy the wedding ring.
`It was a pretty hard job, breaking up this place and making the first crops grow,' he said, pushing back his hat and scratching his grizzled hair. `Sometimes I git awful sore on this place and want to quit, but my wife she always say we better stick it out. The babies come along pretty fast, so it look like it be hard to move, anyhow. I guess she was right, all right. We got this place clear now. We pay only twenty dollars an acre then, and I been offered a hundred. We bought another quarter ten years ago, and we got it most paid for. We got plenty boys; we can work a lot of land. Yes, she is a good wife for a poor man. She ain't always so strict with me, neither. Sometimes maybe I drink a little too much beer in town, and when I come home she don't say nothing. She don't ask me no questions. We always get along fine, her and me, like at first. The children don't make trouble between us, like sometimes happens.' He lit another pipe and pulled on it contentedly.
I found Cuzak a most companionable fellow. He asked me a great many questions about my trip through Bohemia, about Vienna and the Ringstrasse and the theatres.
He was still, as Antonia said, a city man. He liked theatres and lighted streets and music and a game of dominoes after the day's work was over. His sociability was stronger than his acquisitive instinct. He liked to live day by day and night by night, sharing in the excitement of the crowd.--Yet his wife had managed to hold him here on a farm, in one of the loneliest countries in the world.
I could see the little chap, sitting here every evening by the windmill, nursing his pipe and listening to the silence; the wheeze of the pump, the grunting of the pigs, an occasional squawking when the hens were disturbed by a rat. It did rather seem to me that Cuzak had been made the instrument of Antonia's special mission. This was a fine life, certainly, but it wasn't the kind of life he had wanted to live. I wondered whether the life that was right for one was ever right for two!
I asked Cuzak if he didn't find it hard to do without the gay company he had always been used to. He knocked out his pipe against an upright, sighed, and dropped it into his pocket.


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text:
Kolding to Neumünster train
Overview: Train from Kolding to Neumünster
Average train ticket price $35 (€29)
Trains from Kolding to Neumünster cover the 99 miles (160 km) long trip taking on average 3 h 3 min with our travel partners like. Normally, there are 5 trains operating per day, including direct services available. While the average ticket price for this route costs around $35 (€29), you can find the cheapest train ticket for as low as $35 (€29). Travelers depart most frequently from Kolding and arrive in Neumünster.
Travel Tips: Trains from Kolding to Neumünster
Travel by train to Neumünster easily. Whether you want fast, cheap or something entirely different, our travel experts have collected everything you need to know so you can find the best option from Kolding to Neumünster.
What COVID-19 travel safety information and restrictions should I be aware of for my train between Kolding and Neumünster?
Travel between Kolding, Denmark and Neumünster, Germany by train is: Partially open.
Can I enter Germany from Denmark?
International entry status: Entry is partially open for citizens and permanent residents of Denmark
Do I need to quarantine on arrival in Germany from Kolding?
What are the safety rules to follow in Neumünster, Germany?
All travelers in Germany must observe these coronavirus safety measures:
The information above was last checked on 1/19/22. Remember to review the latest COVID-19 travel safety regulations for your train between Kolding and Neumünster as this information can change.
What is the restriction level for the return leg of a round trip journey from Neumünster, Germany to Kolding, Denmark?
The restriction level for your return train to Kolding, Denmark from Neumünster is: Partially open.
Is my return train into Kolding from Neumünster restricted?
Do I need to quarantine on arrival in Denmark from Neumünster?
Travellers who have recovered from COVID-19 in the last 6 months are exempt from providing a negative COVID-19 test (certificate needed)
What are the safety rules to follow in Kolding, Denmark?
The government of Denmark has imposed these measures to reduce the spread of COVID-19:
Last checked on 1/20/22. Remember to check the latest COVID-19 travel safety regulations for your train to Kolding from Neumünster closer to your date of departure here here.
What is the price of the cheapest train from Kolding to Neumünster?
Omio customers have found cheap train tickets to Neumünster from Kolding for as low as $35 (€29) for the next 7 days.
How much is the train between Kolding and Neumünster on average?
The train price between Kolding and Neumünster is on average $35 (€29) if you are looking to purchase your tickets for this trip in the next 7 days.
What is the distance from Kolding to Neumünster by train?
The train distance from Kolding to Neumünster is around 99 miles (160 km).
How long is a train from Kolding to Neumünster on average?
The train time to Neumünster from Kolding is on average 3 h 3 min for the 99 miles (160 km) long journey, but the time it takes to go between Kolding and Neumünster by train can vary depending on specific dates or traveling on weekends and holidays.
Which train station from Kolding to Neumünster do I depart from? Which Neumünster train station from Kolding do I arrive in?
Some of the Kolding train stations to Neumünster you can start your journey from include Kolding and Kolding, Banegårdspladsen / Slotsalle (togbus). Similarly, some of the arrival train stations in Neumünster include Neumünster, Neumünster Süd AKN and Neumünster Stadtwald.
When traveling this route, Omio customers are departing most frequently from Kolding and arriving in Neumünster.
Where do I find the Kolding train station to Neumünster? Where is the Neumünster train station?
Passengers board the train most frequently from Kolding, which is located around 0.4 miles (593 m) away from the city center, and they get off the train at Neumünster, located 0.1 miles (170 m) away from the city center.
How many train services are there between Kolding and Neumünster a day?
On average, there are 5 trains a day from Kolding to Neumünster. The train times and services may be different on weekends and holidays compared to weekdays.
How early should I book train tickets between Kolding and Neumünster to score the best deals?
You can find trains to Neumünster from Kolding to cost on average $35 (€29) one way if you book within the next 7 days. But we recommend buying train tickets in advance to score the best deals and save money on your journey. You'll see tickets for the Kolding to Neumünster train generally on sale a few months before the planned travel date.
Kolding is the most popular Kolding railway station for Omio travelers, but it's not the only one. Read all the information you need to know about the main train stations in Kolding for your trip to Neumünster.
Kolding, Banegårdspladsen / Slotsalle (togbus)
More options for your journey from Kolding to Neumünster
More information on how to get to Kolding Train Station(s)
Tickets and more information for trains to Neumünster
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Train Hanover-Neumünster
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Train Kassel-Neumünster
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text:
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Message From Department Head
Doeun Choe, Ph.D., P.E.
Hernandez Hall, Room 213
dchoe@nmsu.edu
Ph.D. in in Civil Engineering/Structures 2007, Texas A&M University (College Station) U.S.
M.S. in Architectural Engineering/Structural Engineering 2002, Inha University, South Korea
B.S. in Architectural Engineering 2000, Inha University, South Korea
Jan 2021 to Present - Assistant Professor, New Mexico State University, NM
September 2013 to December 2020 - Assistant Professor, Prairie View A&M University (PVAMU), TX
June 2012 to May 2013 - Adjunct Assistant Professor (FT), PVAMU, TX
August 2011 to May 2012 - Senior Staff Engineer, MMI Engineering & Adjunct Assistant Professor (PT), PVAMU, TX
June 2008 to August 2011 - Senior Staff Engineer, MMI Engineering, Inc., Houston TX
May 2004 to December 2007 - Research Assistant, Texas A&M University, College Station, TX
Artificial Intelligence and Deep Learning
Probabilistic Modeling & Structural Reliability
Deterioration and Resilience of Civil Infrastructures
Structures Extreme Environmental Conditions
Choe, D. E., Kim, H. C., & Kim, M. H. (2021). Sequence-based modeling of deep learning with LSTM and GRU networks for structural damage detection of floating offshore wind turbine blades. Renewable Energy, 174, 218-235.
Kim, C., Choe, D., Castaneda, H. (2020). Probabilistic Corrosion Initiation Models for Coastal Concrete Structures Corrosion and Materials Degradation, 1(3), 328-344.
Kim, H. C., Kim, M. H., & Choe, D. E. (2019). Structural health monitoring of towers and blades for floating offshore wind turbines using operational modal analysis and modal properties with numerical-sensor signals. Ocean Engineering, 188, 106226.
Choe D., Gardoni P., Rosowsky D., and Haukaas T. (2009). Seismic Fragility Estimates for Reinforced Concrete Bridges Subject to Corrosion., Structural Safety, 31(4), 275-283.
Choe, D., Gardoni, P., Rosowsky, D., and Haukaas, T. (2008). Probabilistic Capacity Models and Seismic Fragility Estimates for RC Columns Subject to Corrosion., Reliability Engineering & System Safety , 93(3), 383-393.
David Jauregui, Ph.D., P.E.
Nirmala Khandan, Ph.D., P.E.
Craig M. Newtson, Ph.D.
Lambis Papelis, Ph.D.
Pei Xu, Ph.D.
Paola Bandini, Ph.D., P.E.
Salim Bawazir, Ph.D.
Douglas Cortes, Ph.D.
Huiyao Wang, Ph.D.
Ehsan Dehghan-Niri, Ph.D.
Yanyan Zhang, Ph.D., P.Eng.
Ken White, Ph.D., P.E
Lakshmi N. Reddi, Ph.D., P.E.
Huidae Cho, Ph.D., P.E., CFM, GISP
Umaima Al Aqtash, Ph.D.
Qianyun (Gloria) Zhang, Ph.D.
civil@nmsu.edu
Hernandez Hall
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Las Cruces, NM 88003-8001
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text:
The BigChilli TV
Globally acclaimed national landmark "ICONSIAM" to celebrate prosperous first anniversary with mega event "The Celebrations of Glory ICONSIAM" complete with 3-day continuous phenomenal activities and entertainments on November 8 – 10, 2019
To further reinforce Thailand's stature on the global stage and ICONSIAM as Global Destination, the nationwide collaboration project to develop the Chao Phraya riverside and Thonburi communities "ICONSIAM" celebrates its 1st anniversary as Thailand's symbol of prosperity with "The Celebrations of Glory ICONSIAM", 3-day continuous celebrations of phenomenal activities and entertainment that will be a feast for the eyes of the world between November 8 – 10, 2019 from 10:00 a.m. – 10:00 p.m. at ICONSIAM – Charoen Nakhon Road.
Mrs. Chadatip Chutrakul, Director of ICONSIAM Co., Ltd., said, "We are very proud to have fulfilled our important mission announced seven years ago. We have proven that ICONSIAM is a game-changing destination which has successfully turned the Chao Phraya River and the Thonburi side of the city into one of Bangkok's business and tourism hubs, spreading prosperity to surrounding communities and businesses while becoming a key factor behind the rapid rise of Thonburi as a metropolis. Additionally, ICONSIAM has been recognized for its major contribution to tourism as a new and powerful tourism magnet and a global destination by the Chao Phraya River attracting visitors from around the world and Thailand."
With considerable investment and global marketing efforts ICONSIAM has become a must-visit destination and proven to be a project that is contributing to the strengthening of Thai economy and all levels of the surrounding communities. Moreover, it has been cited as a model retail development where shared value has successfully been created and effectively spread prosperity into all levels from surrounding communities, to society, and the country with the nation's sustainable economy and growth in mind. The Chao Phraya riverside destination featuring elegant and sophisticated design work combines arts and traditions and express them in exemplary ways as never before through infinite activities and entertainment by locals, national, and global players alike. With extraordinary shopping retails, restaurants and luxury hotels ICONSIAM has excellently impressed all visitors in its first blossoming year and has truly reinforced its 'the best of Thailand meets the best of the world' concept.
"The great success of ICONSIAM is the result of the greatest collaboration of creative forces of our time. It's from the hearts of thousands of Thais together with experts from four continents and 15 nations. They have contributed as the makers, the co-creators and the supporters. They are architects, engineers, interior decorators, artists, designers, businessmen and people from communities around the country. All the success and wonders of ICONSIAM today is credited to everyone involved in the project," said Mrs. Chutrakul.
In celebration of its 1st anniversary, ICONSIAM organizes for the mega super event "The Celebrations of Glory ICONSIAM. There are continuous celebrations between November 8 – 10, 2019 with extraordinary light and sound spectacles on the Chao Phraya River that will be a feast for the eyes of the world too further reinforce its 'the best of Thailand meets the best of the world' concept.
On Friday November 8, enjoy the "Glory of ICONSIAM" show in series Rhythm of Success, Glory of Memories, and Happiness of Extraordinary performed by professional actors and actresses including Nadech Kugimiya and Urassaya Sperbund. Prepare to meet, World-class singer, Matteo Bocelli who will join the Grand Opening event of one of the Seven Wonders – TRUE ICON HALL (The True Icon Experiences of Imagination), alongside several Thai artists including Thiti Mahayotaruk, Nont Tanont etc. This first ever world-class conference center designed to the highest international standards will make history in Thailand with a seating capacity of 2,700 on the 7th floor of ICONSIAM. With the capability to support conferences and world-renowned performances with the best technology in Asia, TRUE ICON HALL will help make Bangkok a hub for international conferences and leading shows of the world. On Saturday November 9, revel in beautiful melodies with Thailand's top diva Mariam B5 and Q FLURE then on Sunday November 10, delight in the mini concert by the crowd-pleasing Atom Chanakan.
As for SIAM Takashimaya, the glorious 1st anniversary will be celebrated throughout November with 'Glory Hokkaido Celebration'. Popular tourist attractions and landmarks of Hokkaido will be simulated for visitors to see up close and personal. These include a field of lavender and other colorful flora, an Ikebana exhibition, a Sapporo food hall complete with famous shops straight out of Hokkaido to Thailand for the first time, an exciting dance show by the Sapporo Yosakoi Soran which will be flown straight from Hokkaido specifically for the event, a giant 100-kg Maguro by an award-winning chef, a Ben Chalatit mini concert, and a super special promotion with more than THB 1 million worth of prizes up for grabs.
While SOOKSIAM, the town of Thai joy, is getting 7 Thai heroes ready for the world stage and preparing to celebrate its 1st anniversary with "The Celebration of One Year of Seven Happiness's at Town SOOKSIAM of ICONSIAM". Awaiting visitors will experience a range of activities such as Taste and Shop with 20 top business owners from over 40 shops of the year, performances from national art masters such as Santi Lunpe, Buason Thanomboon, Banyen Rakgan, Kloaw Rojanamethakul and a concert from Ben Chalatit. On the full-moon night, all are invited to join in the Loy Krathong tradition and a beauty contest for women in three age groups. These activities will be between November 8-11, 2019. On November 9, LOCAL HERO awards will be presented to the outstanding community shops which are able to generate strong sales and impress visitors by keeping them happy and promoting Thai identity to the world. On November 10, OSMEP's Local to Global winners will be announced. On November 11, visitors are invited to join in the Loy Krathong tradition with a wide range of promotions offered.
Let's celebrate the mega success with Thailand's phenomenal activities and entertainments at "The Celebrations of Glory ICONSIAM" for 3 continuous days between November 8 – 10, 2019 at ICONSIAM, Charoen Nakhon Road. Free entrance!! All are invited to join the world's best super event with a multitude of historical performances. For more information, call 1338 or visit www.iconsiam.com.


This card class and video are a fabulous example of what happens when the Stampin' Up! Animal Outing Suite meets the January Paper Pumpkin kit. It's an adorable mix of animals and fun.
I've created 2 of these cards with pieces from the kit, and the hippo was created with the Animal Outing Suite in the catalog. Showing these alternates can be made with the January kit, and/or with regular catalog products if you don't have the kit (the kit and refills have sold out).
Video: I will be recording this class video live at noon EST today. It's free to join in live and be part of the fun, win prizes and more. If you can't make it live, this video replay will always be available here on my blog, Facebook and/or Youtube.
Prize Patrol! I've got a mega-giveway, not only will I be giving away a couple of these "sold out" kits, I'm also giving away 2 full Animal Outing Bundles. Comment on the video to enter. I'll be drawing prizes for both live and replay viewers.
Stamp Case Inserts – I now have downloadable stamp case inserts for September 2018– January 2019 posted below. I will post these inserts each month with my videos.
FREE GRAB BAGS – Want everything in the new Stampin Up Occasions or Annual Catalog? Join my VIP online stamp club and start collecting on budget and receive free gifts. Join now through February 28 and receive a Free Grab Bag of new Stampin Up products from me as a bonus gift!
Here are the chapters of this online class video in case you'd like to skip ahead. This video also contains closed captions for the hearing impaired.
February's Paper Pumpkin kit will feature beautiful succulent flowers. It will make 9 full sized cards (3 each of 3 designs).
This is a video comment entry giveaway. Winner drawn on February 22. To enter, simply click over to the video on Facebook or Youtube, and leave a comment. No purchase necessary.
I love these cards! Soooo cute!
I've fallen in love since watching your online! Now on my list so hopefully they will have some come in. Loved your tip on picking color up with the color remover pen.
Loved your Outing cards, great job.
OMG, those cards are absolutely adorable!! Love watching your videos!!


text:
Archival materials (251)
Diaries (20)
Sketches (19)
Records (documents) (9)
Art museums (35)
Portraits, American (11)
Museum loans (10)
Museum registrars (10)
Mural painting and decoration (7)
Hirshhorn Museum and Sculpture Garden. Office of the Registrar (6)
National Portrait Gallery. Office of Exhibitions (6)
Metropolitan Museum of Art (New York, N.Y.) (5)
Museum of Modern Art (New York, N.Y.) (5)
Thayer, Abbott Handerson (5)
Hassam, Childe (4)
Sheeler, Charles (4)
Smithsonian Institution (4)
Wyeth, Andrew (4)
Art Institute of Chicago (3)
Bertoia, Harry (3)
Bishop, Isabel (3)
Brush, George de Forest (3)
Garden Club of America (3)
Gonzalez, Xavier (3)
Greenberg, Clement (3)
Hopper, Edward (3)
Abenaki Indians (1)
Algonquian Indians (1)
Catawba Indians (1)
Chickahominy (1)
Christian Scientists (1)
Indians of Central America (1)
Innu Indians (1)
Kitigan Zibi Anishinabeg (Maniwaki Algonquin) [River Desert] (1)
Machapunga (Pungo River) (1)
Malecite Indians (1)
Massachuset Indians (1)
Mattaponi (1)
Micmac Indians (1)
Art, Modern (1)
Bhaktapur (Nepal) (1)
Breeze Hill (Harrisburg, Pennsylvania) (1)
Busia District (Kenya) (1)
Canadian Rockies (B.C. and Alta.) (1)
Chesapeake Bay (Md. and Va.) (1)
Cincinnati (Ohio) (1)
Corinth (Miss.) (1)
DeKalb (Ill.) (1)
Enid A. Haupt Garden (Washington, D.C.) (1)
Archives Center, National Museum of American History (80)
Smithsonian Institution Archives (74)
Eliot Elisofon Photographic Archives, National Museum of African Art (1)
Query: Art museums -- Connecticut -- New London
251 records — Page 14 of 26
Smithsonian Associates
3.82 cu. ft. (1 record storage box) (1 document box) (4 tall document boxes)
This accession consists of press releases and news articles pertaining to the Lecture and Seminar Program. Also included are videocassettes of "Crossroads of Continents" and photographs of different Smithsonian events across the nation and world.
Warshaw Collection of Business Americana Subject Categories: Agriculture
Warshaw, Isadore, 1900-1969
9.93 Cubic feet (consisting of 21 boxes, 9 folders, 12 oversize folders, 3 map case folders, plus digital images of some collection material.)
NMAH.AC.0060.S01.01.Agriculture
A New York bookseller, Warshaw assembled this collection over nearly fifty years. The Warshaw Collection of Business Americana: Agriculture forms part of the Warshaw Collection of Business Americana, Subseries 1.1: Subject Categories. The Subject Categories subseries is divided into 470 subject categories based on those created by Mr. Warshaw. These subject categories include topical subjects, types or forms of material, people, organizations, historical events, and other categories. An overview to the entire Warshaw collection is available here: Warshaw Collection of Business Americana
Exhibition Records
National Portrait Gallery. Office of the Registrar
5 cu. ft. (5 record storage boxes) (1 document box)
This accession consists of the files created by the Office of the Registrar in the course of their work on fifteen exhibitions shown between 1982 and 1991, including Peace and Friendship: Indian Peace Medals in the United States, on view from January through July 1985; Charles Willson Peale and His World, November 1982 through January 198...
Cooper-Hewitt Museum. Public Information Office
This accession consists of general correspondence and memoranda with advertising agencies, corporations, Smithsonian staff, and television and radio stations concerning announcements and public service notices of museum events and activities; memoranda with staff concerning museum contributions to Smithsonian publications; press releases; ...
Warshaw Collection of Business Americana Subject Categories: Steamboats [Ships, Boats, and Vessels]
10.22 Cubic feet (consisting of 20 boxes, 2 folders, 9 oversize folders, 3 map case folders, 3 flat boxes (2 full, 1 partial.))
NMAH.AC.0060.S01.01.Steamboats
A New York bookseller, Warshaw assembled this collection over nearly fifty years. The Warshaw Collection of Business Americana: Accounting and Bookkeeping forms part of the Warshaw Collection of Business Americana, Subseries 1.1: Subject Categories. The Subject Categories subseries is divided into 470 subject categories based on those created by Mr. Warshaw. These subject categories include topical subjects, types or forms of material, people, organizations, historical events, and other categories. An overview to the entire Warshaw collection is available here: Warshaw Collection of Business Americana
Central Administrative Records
National Portrait Gallery. Administrative Office
14 cu. ft. (14 record storage boxes)
This record unit documents the activities and efforts of the Administrative Office to acquire objects and portraits, most notably correspondence with art collectors and professional artists. The records include correspondence and memoranda with various art collectors, professional artists, domestic and foreign museums, educational institutions...
Warshaw Collection of Business Americana Subject Categories: Paper Products
NMAH.AC.0060.S01.01.Paper
A New York bookseller, Warshaw assembled this collection over nearly fifty years. The Warshaw Collection of Business Americana: Paper Products forms part of the Warshaw Collection of Business Americana, Subseries 1.1: Subject Categories. The Subject Categories subseries is divided into 470 subject categories based on those created by Mr. Warshaw. These subject categories include topical subjects, types or forms of material, people, organizations, historical events, and other categories. An overview to the entire Warshaw collection is available here: Warshaw Collection of Business Americana
National Portrait Gallery. Office of Exhibitions
10 cu. ft. (9 record storage boxes) (2 document boxes)
This accession consists of records that pertain to eight exhibitions which the Office of Exhibitions organized between 1983 and 1991. The bulk of the records includes correspondence between the National Portrait Gallery (NPG) Director, Alan Fern, and various national and international museum institutions, donors, art galleries, archives, ...
Underwood & Underwood Glass Stereograph Collection
Underwood & Underwood
160 Cubic feet
The major part of the collection, series 1-4, contains nearly 28,000 glass plates, including original stereoscopic negatives, interpositives, and both negative and positive non-stereoscopic plates used to produce lantern slides and paper prints. The photographs were taken all over the world. The majority are from the Underwood & Underwood active fi...
Frank Espada Photographs
Espada, Jason
Espada, Frank, 1930-
17 Cubic feet (52 boxes)
Collection consists of photographic materials taken by Frank Espada, mostly images from the Puerto Rican Diaspora Documentary Project, which documents these communities across the Unites States. In addition, there are materials relating to his earlier work documenting civil rights activities, also in the United States during the 1960s and 1970s.


text:
Q: CSS/JQuery menu navigation What code or script am I looking for in order to sticky a menu to the top of the website even as the user scrolls down the page?

A: position: fixed
Only use this for horizontal menus though — otherwise links to document fragments will put the content you are linking to under the menu.
Consider not using this, scrolling back up to the top is easy, and screen real estate is valuable (especially on a small display, such as a laptop).

A: You are looking for fixed positioning.
#someMenu {
  position:fixed;
}

From the documentation position fixed:

Generates an absolutely positioned element, positioned relative to the browser window. The element's

A: #idOfElementToFix {
  position: fixed;
  top: 10px; /* 10px from top of browser viewport */
  right: 10px; /* 10px from right of browser viewport */
}

Bear in mind that this could easily end up covering other elements as the user scrolls the page, so it's best to leave an empty gutter for it to occupy.
Just as food for thought, here's a link to one of the better tutorials for such a thing, by Remy Sharp: jQuery for Designers

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction}
With the great success of deep learning in various fields, there is an increasing interest to apply deep learning to physical problems. This implies learning physical equations, which can be used as a model to control robots \cite{planning_trajectories} or to solve numerical problems \cite{Raissi2018DeepHP, SIRIGNANO20181339}. In this work we propose a method to first predict the flow field for a given physical setup. Based on this, the shape of an object is estimated from physical quantities calculated on the predicted flow field. This framework for instance can be used to design airfoils for hydraulic machines. For a given set of fluid dynamical properties, e.g. forces on the airfoil surfaces, the system can estimate a shape of the airfoil to match these properties.\\
\indent
Especially the simulation of fluid flows using numerical solvers is a challenging task, which requires a strong understanding of the problem domain and complex mathematical models. In general, such physical systems can be characterized by a system of coupled non-linear partial differential equations (PDEs). In recent years several deep learning approaches \cite{DBLP:journals/corr/abs-1810-08217, 10.5555/3305890.3306035, Xie2018tempoGANAT} have shown promising results in the field of inference of fluid flow simulations in terms of computational time and prediction accuracy.\\
\indent
These approaches \cite{Lagaris_1998, Raissi2018DeepHP, Aarts_2001, SIRIGNANO20181339} are either designed to solve a specific PDE for a defined problem subject to boundary conditions to infer the temporal evolution of the system. Or they are designed as data driven models \cite{10.5555/3305890.3306035, Xie2018tempoGANAT, schenck2018spnets, Ummenhofer2020Lagrangian}, which aim to learn the underlying physical behaviour of fluid dynamics from data. These models can be used to infer the flow field (e.g. estimating the velocity field or fluid motion) for another problem setup. The data-driven models in general differ with respect to their representation of the fluid. This includes the representation of the flow field on a Cartesian grid so that image processing algorithms can be applied \cite{DBLP:journals/corr/abs-1810-08217, 10.1145/2939672.2939738}. In common numerical solvers the flow field is represented as a mesh of arbitrary polygons, which can be processed with graph neural networks \cite{wu2019comprehensive}. Further, the fluid can be treated as particles, which can be seen as a point cloud \cite{schenck2018spnets, Ummenhofer2020Lagrangian}.
\begin{figure}[t]
	\center
	\def\svgwidth{250pt}
	\input{CombinedModel2.pdf_tex}
	\caption{Combined model with a pretrained U-Net to predict the flow field for a given input geometry and a Spatial Transformer Network (STN) in front to optimize the input geometry subject to physical constraints calculated on the predicted flow field.}
	\label{combinedModel}
\end{figure}\\
\indent
In this work we focus on a data-driven model on a Cartesian grid. To train the model several hundred CFD-simulations of a channel flow with objects of different shapes and order inside the channel are used as true data. In a preprocessing step they get interpolated onto a regular grid, so that a convolutional neural network (CNN) can be used to process the data. The main goal of this work is to connect physical equations that depend on the flow field with a neural network and show how the input geometry can be manipulated with respect to these equations.\\
\indent
In a first step a well established system \cite{DBLP:journals/corr/abs-1810-08217} based on a U-Net \cite{DBLP:journals/corr/RonnebergerFB15} architecture is used to learn the fluid dynamics and to infer the flow field for a given new geometry setup. On the basis of these solutions we are able to calculate meaningful equations which describe the system, e.g. the total pressure difference or the forces on the objects. These equations are further used as physical constraints for the shape optimization.\\
\indent
In a second step a \textit{Spatial Transformer Network}~(STN)~\cite{DBLP:journals/corr/JaderbergSZK15} is used to manipulate the input object to control the equations of interest. Since this method is fully differentiable the gradients of the equations calculated on the out coming flow field can be propagated back to the input geometry. With this gradient information the STN is able to change the shape of the object according to the given equations.\\
\indent
For the optimization a two-step training process is used. First, the U-Net gets trained in isolation to learn the inference of the flow field. Second, the U-Net and the STN act as a combined model, where the parameters of the U-Net are frozen. Thus, only the transformation of the input shape will be optimized, while the performance of the flow field prediction will be kept constant. The combined model is depicted in Figure \ref{combinedModel}.\\
\indent
This method can be seen as a kind of inverse design process which in general presents major challenges in terms of numerical algorithms, computational time and convergence. From the forward pass, a flow field is obtained where the specified constraints can be calculated. Afterwards in the backward step the input shape gets transformed to fulfil these constraints.\\
\indent
Besides using a STN to transform the shape it is also possible the use a GAN \cite{NIPS2014_5423} architecture to generate the optimal shape from a noise vector. Nevertheless this method can lead to scattered geometries over the whole channel. With the STN it is possible to prevent this by using a properly initialized geometry that retains the transformed geometry as a solid object.\\
\indent
In contrast to the presented approach, other inverse design methods \cite{SUN2015415, Nanophotonic_Structures} are using a direct mapping from a fixed set of geometry parameters to given physical quantities. These methods require retraining and new datasets in case of changing geometry parameters or physical quantities. These methods may outperform the presented approach for a fixed setup but require retraining and new datasets in case of changing geometry parameters or physical quantities. So these models are not flexible. Our proposed method is more general, since it can reuse the estimation of the flow field in case of a changing geometry setup and is not limited by predefined set of geometry parameters. Based on this solution varying physical quantities can be calculated. Thus, we have a transferable model which can be applied to a wide range of problem configurations.\\
\\
\indent
The contributions of our work are summarized below:
\begin{itemize}
 \item A fully differentiable flow prediction framework based on a U-Net architecture in combination with a STN is proposed to optimize the shape of the input geometry with respect to physical constraints calculated on the predicted flow field.
 \item The framework is successfully applied to generic objects such as rectangles, triangles and circles, and more realistic objects such as airfoils for different physical equations implying the total pressure difference, object forces, geometric restrictions and the full flow field.
 \item Our method relies on predicting the flow field in a first step and hence can be used for varying physical quantities and geometry parameters. Thus, a transferable model is developed for a wide range of setups.
 \item Our dataset is available at \textbf{https://github.com/Flow-Field-Prediction/2D-Channel-Flow} for experiments and further studies.
\end{itemize}
\section{Related Work}
There are a few approaches which can be used to predict the flow field for a given setup. A major group is approximating the unknown solution of PDEs to satisfy the boundary and initial conditions. Scattered observation with spatial and temporal coordinates~($x$, $t$) are used as input to predict the corresponding output values~$u=f(x,t)$. To learn the underlying PDE, the solution of the PDE~$J(f(x,t))$ is used as loss function, thus~$J(f)$ measures how well~$f(x,t)$ satisfies the PDE. The concepts mainly differ on how to approximate the derivatives of the PDEs, e.g.~$\frac{\partial u}{\partial x}$, $\frac{\partial u}{\partial t}$. The ability of a fully differentiable network is used in \cite{Lagaris_1998, Raissi2018DeepHP, raissi2018hidden} to propagate the predicted output~$u$ back to the inputs~$(x,t)$ to get the derivatives. In \cite{Aarts_2001} separate linear layers are used to approximate the particular derivatives and connect them to model the solution of the PDE. In contrast, the first order derivatives can be calculated analytically and a Monte-Carlo method is used to approximate the second order derivatives~\cite{SIRIGNANO20181339}. These methods can be used to infer the solution for a further time horizon or to learn a general solution for a wide range of boundary, initial and physical conditions.\\
\indent
Another type of approaches does not use the underlying PDEs, instead the fluid dynamics are learned from a large amount of data with the use of certain distance measures between the predicted and the true flow field. Thus, a model should be trained to learn a generalized solution of the fluid dynamics to infer the solution of the flow field for new setups. In \cite{10.1145/2939672.2939738, DBLP:journals/corr/abs-1810-08217} the data is stored on a regular two-dimensional grid to be processed with common convolutional neural networks~(CNN) by optimizing the mean square error (MSE). These very basic concepts are used in this work for the flow field prediction, since we focus on the shape optimization. The prediction of the flow field can be replaced by more complex methods in a further work. An extension onto the three-dimensional case is presented in \cite{10.5555/3305890.3306035, Kim2018DeepFA, Latent_Space_Physics, Xie2018tempoGANAT}. These methods also provide the ability of learning the temporal evolution of fluid flows.\\
\indent
Besides the representation of data as a regular grid, the fluid can also be treated as particles and stored as a point cloud. In \cite{schenck2018spnets, Ummenhofer2020Lagrangian} new types of convolution layers are introduced to process point clouds to predict fluid motion. These models are further able to adapt fluid parameters to moving objects and boundaries.\\
\indent
In the past several methods for inverse design of geometries were presented. In \cite{doi:10.2514/1.J057894} the graph of the pressure distribution~$p(x)$ on the surface of an airfoil over its \mbox{$x$-coordinates} is used as input for a CNN to predict the corresponding \mbox{$y$-coordinates} of the target airfoil shape. Another approach~\cite{SUN2015415} uses a neural network (NN) to link a large amount of aero-dynamic quantities with geometry data. They use different parametrizations to represent the geometry information.
In \cite{Nanophotonic_Structures} structural parameters~$D$ are transformed to electromagnetic responses~$\hat{R}$. First a model is trained to map from~$D$ to~$\hat{R}$, then freezing the weights. Afterwards another network is stacked in front of it to learn the mapping from~$R$ to~$D$ to~$\hat{R}$, while minimizing the~$MSE(R,\hat{R})$. Thus, using~$R \rightarrow D$ in isolation the structural parameters~$D$ for a specified electromagnetic response~$R$ can be predicted. We also use a pretrained model for the mapping from geometry information to physical response, but extend it further, as we iteratively transform the geometry to obtain a direct response in terms of the physical quantities defined over the entire fluid field.
It has to be mentioned that these methods are using a fixed predefined set of input features and corresponding geometric representations. Thus, a new dataset and retraining is required in the case of changing features, so they are not directly comparable to our approach. In contrast our approach has a transferable model and can be used for changing problem configurations.
\section{Methodology}
In this section we present an overview of the proposed method for learning the fluid dynamics and predicting the flow field for new setups. Afterwards the Spatial Transformer Network (STN) is presented to change the shape of the input objects. These concepts are then coupled to propagate gradients of the loss function calculated on the predicted flow field back to the input object. Thus, it is possible to change its shape with respect to physical quantities defined by the loss function. In the last step different physical quantities and their associated equations are highlighted.
\subsection{Dataset}
\begin{figure}[t]
\center
\begin{tabular}{cc}
  \includegraphics[width=40mm]{img/geo_circle_square_crop2.eps} & \includegraphics[width=40mm]{img/geo_airfoil_crop2.eps}\\
  \includegraphics[width=40mm]{img/u_circle_square_crop.eps} &  \includegraphics[width=40mm]{img/u_airfoil_crop.eps}\\
  \includegraphics[width=40mm]{img/v_circle_square_crop.eps} & \includegraphics[width=40mm]{img/v_airfoil_crop.eps}\\
  \includegraphics[width=40mm]{img/p_circle_square_crop.eps} &  \includegraphics[width=40mm]{img/p_airfoil_crop.eps}\\
\end{tabular}
\caption{Samples from the dataset interpolated to images. \textit{Top}:~Geometry. \textit{Bottom}: Flow field with three channels $u$,~$v$,~$p$.}
\label{dataset}
  \begin{textblock}{0.5}(1.13,1.68)
    $u$
  \end{textblock}
  \begin{textblock}{0.5}(1.13,2.31)
    $v$
  \end{textblock}
  \begin{textblock}{0.5}(1.13,2.935)
    $p$
  \end{textblock}
  \begin{textblock}{0.5}(4.5,1.68)
    $u$
  \end{textblock}
  \begin{textblock}{0.5}(4.5,2.31)
    $v$
  \end{textblock}
  \begin{textblock}{0.5}(4.5,2.935)
  $p$
  \end{textblock}
\end{figure}
The simulation of fluid flow is a challenging task since it requires a complex mathematical model to capture changing motions and boundary conditions in a complex domain. Such systems are in general modelled as a system of coupled non-linear PDEs. An established physical formulation to describe fluids are the \textit{Navier-Stokes Equations}~(NSE)
\begin{equation}
 \frac{\partial}{\partial t}(\rho \textbf{u}) + \rho \textbf{u} \cdot \nabla \textbf{u} = - \nabla p + \mu \nabla^2 \textbf{u} + \rho \textbf{g},\;\;
 \nabla \cdot \textbf{u} = 0,
\end{equation}
with fluid velocity~$\textbf{u}$, pressure~$p$, external forces~$\textbf{g}$, density~$\rho$ and dynamic viscosity~$\mu$. To solve this system of equations numerical methods such as finite-differences, finite-volumes or finite-elements are used. These methods require a discretization of the domain. Common techniques are grid-like structures to model the interaction inside the fluid.\\
\indent
To learn the fluid dynamics with a neural network, a large amount of fluid simulations is required as training data. In this work the simulations are done with FEniCS \cite{AlnaesBlechta2015a}, which uses a finite-element method to solve the PDEs. FEniCS has an automatic process to mesh the domain with unstructured triangular elements. Every node in the mesh holds values for the velocity in $x$- and $y$-direction~($u,v$) and the pressure~$p$, all together representing the flow field. To use this as input for a convolutional neural network, the point set of nodes of the unstructured mesh are linearly interpolated to a Cartesian grid~$V \in \mathbb{R}^{H\mathrm{x}W\mathrm{x}C}$. This represents the three values~$u$,~$v$~and~$p$ of the field with height~$H=64$, width~$W=256$ and number of channels~$C=3$. Each element of the Cartesian grid can be interpreted as a pixel, thus common convolutional layers can be used to process these data. The size of $V$ is chosen such that the original aspect ratio of the channel is kept and enough details of the fluid flow are captured. Two examples for the interpolated flow fields are shown in Figure \ref{dataset} with the three channels $u$, $v$ and $p$, respectively. The parts in the flow field where the geometry is placed are highlighted in black. In the data matrix $V$ these parts are filled with zeros. The flow field on the right side is showing a typical behaviour for an airfoil with high velocity components $u$ in $x$-direction on the top side and lower velocities below which results in a low pressure area above the airfoil.\\
\indent
Before a fluid simulation can be done, the domain has to be modelled i.e., the walls and solid objects inside the domain have to be defined. In this work a 2D~channel flow is used as simulation domain, which has a wall at the top and the bottom and some immersed objects inside the channel. This geometry information stored on the unstructured mesh is also interpolated on a Cartesian grid~$G\in \mathbb{R}^{H\mathrm{x}W\mathrm{x}1}$ as a geometry map with~$C=1$, where a~0 indicates fluid and a~1 represents solid objects. The linear interpolation is leading to blurry border regions between the objects and the fluid, which are rounded to 0 and 1. All simulations in the dataset are stationary 2D~channel flows with a varying number of objects~$n\le3$, randomly placed inside the channel. Objects can be simple geometric forms such as squares, rectangles and triangles as well as more complex shapes such as airfoils.\\
\indent
The dataset~$D=\{(G^i,V^i)|i=1,\ldots,N\}$ consists of pairs of geometry~$G$ and flow field~$V$ with a total amount of~$N=1350$ samples. Thus, the geometry~$G$ is used as input for the network, while the flow field~$V$ is the ground truth for training the model in a supervised fashion. The data is split to have 1050~samples for training the model and 300~samples for evaluation.
\subsection{Flow Field Prediction}
\begin{table}[t]
\begin{center}
\caption{The different stages of the U-Net architecture. The notation ''3x3 Conv(stride=1,pad=1)x$C$ - leakyReLU(0.1)'' denotes a convolutional kernel with filter size~3x3 and $C$~output channels, followed by a leakyReLU activation with slope~${s=0.1}$.}
\label{UNet_architectur}
 \begin{tabular}{l l}
 \hline
 \multicolumn{1}{l}{Layer Name} & \multicolumn{1}{c}{Settings}\\
 \hline\hline
 Input & Geometry Map ${H\mathrm{x}W\mathrm{x}1}$\\
 \hline
 Comp. Stage & \begin{tabular}{@{}l@{}}3x3 Conv(stride=1,pad=1)x$C$ - leakyReLU(0.1) \\
					     3x3 Conv(stride=1,pad=1)x$C$ - leakyReLU(0.1) \\
					     2x2 Pooling(stride=2,pad=0)\end{tabular}\\
 \hline
 Bottom Stage & \begin{tabular}{@{}l@{}}3x3 Conv(stride=1,pad=1)x$C$ - leakyReLU(0.1) \\
					     3x3 Conv(stride=1,pad=1)x$C$ - leakyReLU(0.1)\end{tabular}\\
 \hline
 Exp. Stage & \begin{tabular}{@{}l@{}}2x2 TranspConv(stride=2,pad=2)x$C$ - leakyReLU(0.1) \\
				      Concatenate with corresponding Comp. Stage\\
				      3x3 Conv(stride=1,pad=1)x$C$ - leakyReLU(0.1)\\
				      3x3 Conv(stride=1,pad=1)x$C$ - leakyReLU(0.1)\end{tabular}\\
 \hline
 Output & Flow Field ${H\mathrm{x}W\mathrm{x}C}$\\
 \hline
\end{tabular}
\end{center}
\end{table}
\begin{table}[t]
	\begin{center}
	\caption{Architecture of the Localization Network.}
	\vspace{-1\baselineskip}
	\label{LocNet_architecture}
		\begin{tabular}{l l}
			\hline
			\multicolumn{1}{l}{Layer Name} & \multicolumn{1}{c}{Settings}\\
			\hline\hline
			Input & Geometry Map ${H\mathrm{x}W\mathrm{x}1}$\\
			\hline
			Conv1 & 3x3 Conv(stride=2,pad=1)x64 - leakyReLU(0.2)\\
			\hline
			Conv2, Conv3, Conv4 & 3x3 Conv(stride=2,pad=1)x128 - leakyReLU(0.2)\\
			\hline

			Conv5 & 3x3 Conv(stride=2,pad=1)x64 - leakyReLU(0.2)\\
			\hline
			FC1 & Linear (2054 units) - Tanh\\
			\hline
		\end{tabular}
	\end{center}
\end{table}
To highlight the strong capability of the model in learning the behaviour of fluid flow, no physical prior on the input data such as boundary condition for the velocities and pressure or conservation laws is used. Thus, we simply try to find a mapping~$f(G)=\hat{V}$ from the input geometry~$G$ to the corresponding fluid field~$\hat{V}$. Previous work \cite{DBLP:journals/corr/abs-1810-08217} has already shown strong results in using a U-Net architecture \cite{DBLP:journals/corr/RonnebergerFB15} to learn the dynamics of the fluid from data. We also rely on the \mbox{U-Net} for predicting the flow field, but using a dataset with a large variety of fluid dynamics i.e., various flows, backflows, partial blockage and small gaps. Thus, the network has to capture a wide range of phenomena which makes it challenging to train a suitable model. It can be shown that this method offers promising results regarding the overall error in~($u$,$v$,$p$) and with respect to further analysis of the flow field. This is essential since the main focus of this work is to couple the flow field prediction with a shape optimization subject to physical constraints.\\
\indent
The U-Net is a fully convolutional network described in Table~\ref{UNet_architectur}. Five compression stages are used to reduce the size of the input data, where each has two convolution layers with constant kernel size of~3x3 and doubling channel size~$C=[32,\ldots,512]$ followed by a max-pooling layer and one bottom stage without a pooling layer. Afterwards five expansion stages are applied to get back to the original dimension of the input data. A transposed convolution with a kernel size of~2x2 is used to increase the size of the data with a striding of~2x2. To this the output of the corresponding compression stage is concatenated, followed by two standard convolution layers. The channel size~$C=[512,\ldots,3]$ will be halved per stage, except in the last stage. The activation function leakyReLU with slope~$s=0.1$ is applied, except in the last layer, where the hyperbolic tangent should transform the output to a proper scale. The network is trained with the Adam-optimizer~\cite{kingma2014adam} with a learning rate of~$10^{-4}$ and the sum of squared errors~(SSE) as loss function
\begin{equation}
 \mathcal{L}_{SSE}=\sum_{i=0}^{N}(\hat{V}_i-V_i)^2\;,
\end{equation}
between the predicted flow field $\hat{V}$ and the true flow field~$V$ from the simulations. The SSE is used as loss function to have a strong restriction on every pixel, instead of getting a low average error.
\subsection{Geometry Transformation}
With the presented U-Net architecture it is possible to predict the flow field for a new geometry setup. Since the goal is an interaction of the flow field with a shape optimization subject to physical constraints, it is required to deform the input geometry with respect to the deployed constraints. Therefore a Spatial Transformer Network (STN) \cite{DBLP:journals/corr/JaderbergSZK15} is used.\\
\indent
The STN is a three-steps method. In the first step a localization network~$\theta = f_\mathrm{Loc}(G)$ takes the input geometry map~$G\in \mathbb{R}^{H\mathrm{x}W\mathrm{x}1}$ to compute the parameters~$\theta$ for the transformation~$\tau _\theta$. Depending on the parametrization of the transformation, e.g. an affine transformation, the size of~$\theta$ can vary.\\
\indent
In the next step a parametrized sampling grid is required. The input geometry map is a regular grid~$R={R_i}$ which is a set of points with source coordinates~$R_i=(x^s_i,y^s_i)$. Each element in~$R_i$ defines a pixel in the input geometry map. Then the transformation~$\tau_\theta$ can be applied on~$R$
\begin{equation}
 \begin{bmatrix} x^t_i \\ y^t_i \end{bmatrix}
 = \tau_\theta (R_i) = \mathrm{A}_\theta
 \begin{bmatrix} x^s_i \\ y^s_i \\ 1 \end{bmatrix}\;,
\end{equation}
which puts out a set of points with target coordinates~$(x^t_i,y^t_i)$. The matrix~$\mathrm{A}_{\theta}$ denotes the affine transformation matrix. The height and width of the source coordinates are normalised, such that~$x^s_i, y^s_i \in [-1,1]$. The same interval holds for the target coordinates in the output domain.\\
\indent
In the third step a set of sampling points~$\tau_\theta(R)$ together with the input geometry map~$G$ can then be used to generate a transformed output geometry map~$U\in \mathbb{R}^{H'\mathrm{x}W'\mathrm{x}1}$. This is done with a bilinear sampling kernel of the form:
\begin{equation}
 U^c_i = \sum_{n,m}^{H,W} G^c_{nm} \mathrm{max}(0,1-|x^s_i-m|)\mathrm{max}(0,1-|y^s_i-n|)\;,
\end{equation}
for~$\forall i \in [1,\ldots,H'W']$ and~$\forall c\in [1,\ldots,C]$ to get the output value of every element~$U_i^c$ at the location~$(x^t_i,y^t_i)$ for every channel~$C$.\\
\indent
To deform the input geometry with respect to physical constraints, complex transformations may be necessary. Therefore, the usage of an affine transformation is not sufficient. In this work thin-plate-splines (TPS) \cite{24792, 10.1007/3-540-47977-5_2} are used as a more complex parametrization of the transformation.
\begin{algorithm}[t]
 \begin{algorithmic}[1]
   \State \textbf{Input:}
   \State Train dataset $D=\{(G^i,V^i)|i=1,\ldots,N\}$
   \State New initial geometry map $G_{init}\in \mathbb{R}^{H\mathrm{x}W\mathrm{x}1}$
   \Procedure{Train U-Net}{$G,V$}
   \For {$n$ epochs} {}
   \State Predict Flow Field $\hat{V} = f_{UNet}(G)$
   \State Update $\theta_{\mathrm{UNet}}$ $\leftarrow$ Loss $\mathcal{L}_{SSE}(\hat{V},V)$
   \EndFor
   \State \textbf{return} U-Net parameters $\theta_{\mathrm{UNet}}$
   \EndProcedure

   \Procedure{Initialize Loc-Net}{$G$}
   \For {$n$ epochs} {}
   \State Parameters for Transformation $\theta = f_{Loc}(G)$
   \State Grid Generator $(x^t,y^t)=\mathrm{TPS}(x^s,y^s,\theta)$
   \State Transform Geometry $U=\mathrm{Sampler}(x_t,y_t,G)$
   \State Update $\theta_{\mathrm{Loc}}$ $\leftarrow$ Loss $\mathcal{L}_{SSE}(U,G)$
   \EndFor
   \State \textbf{return} Loc-Net parameters $\theta_{\mathrm{Loc}}$
   \EndProcedure

   \Procedure{Transformation}{$G_{init}$, $\theta_{\mathrm{UNet}}$, $\theta_{\mathrm{Loc}}$}
   \For {$n$ epochs} {}
   \State Transformation parameters $\theta = f_{Loc}(G_{init})$
   \State Grid Generator $(x^t,y^t)=\mathrm{TPS}(x^s,y^s,\theta)$
   \State Transform Geometry $U=\mathrm{Sampler}(x_t,y_t,G_{init})$
   \State Predict Flow Field $\hat{V} = f_{UNet}(U)$
   \State Update $\theta_{\mathrm{Loc}}$ $\leftarrow$ Physical Constraints $\mathcal{L}_{total}(\hat{V})$
   \EndFor
   \State \textbf{return} Transformed Geometry $U$
   \EndProcedure
 \end{algorithmic}
 \caption{Training procedure for geometry transformation}
 \label{pseudoCode}
\end{algorithm}
\\
\indent
The TPS interpolation~$\mathrm{TPS}(x,y)$ is defined over a set of $p$~control points with coordinates~$(x^c_i, y^c_i)$, $i=1,\ldots,p$ which
are chosen among the points of the regular grid~$R={R_i}$ with source coordinates~$(x^s_i, y^s_i)$. The function values~$\mathrm{TPS}(x^s_i, y^s_i)$ then corresponds to target coordinates~$(x^t_i,y^t_i)$. The TPS interpolation has the form
\begin{equation}
\begin{split}
\mathrm{TPS}(x^s,y^s)= &\; \theta_{p+1} + \theta_{p+2}\;x^s + \theta_{p+3}\;y^s \\
& +\sum_{j=1}^p \theta_j T(||(x^c_j, y^c_j) - (x^s,y^s)||)\;,
\end{split}
\end{equation}
where~$T(r)=r^2 \mathrm{log} r$. As for the affine transformation the TPS interpolation has a set of parameters~$\theta$ to control the transformation which are again the outputs of the localization network $f_\mathrm{Loc}$. Afterwards a bilinear sampling kernel as in the original STN paper is applied to get the transformed image.\\
\indent
For the localization network $f_\mathrm{Loc}$ a standard CNN is used, with one regression layer at the end. A detailed description of the network architecture can be found in Table~\ref{LocNet_architecture}. The output dimension of the localization network is depending on the number of parameters which are used for the TPS interpolation. In this work equally distributed control points with a step size of~4 in both spatial dimensions are used. Thus~$p=16\mathrm{x}64$~plus~3 parameters for every spatial dimension are required.
\subsection{Combined Model}
The final model is a combination of the U-Net with the STN in front of it, whereas the U-Net predicts the flow field for a given input while the STN deforms the input repeatedly. The overall training procedure for the geometry transformation is summarized in Algorithm \ref{pseudoCode}. The training of this model is done in a two stage procedure. First the U-Net is trained in isolation to learn a mapping from input geometry $G$ to flow field $\hat{V}$. Afterwards the U-Net and the STN are used in combination. At this point the parameters~$\theta_{\mathrm{UNet}}$ of the U-Net are frozen and only the parameters~$\theta_{\mathrm{Loc}}$ of the STN are updated to perform the transformation of the input. Since this method is fully differentiable from the predicted flow field back to the input geometry, the STN learns how to transform the shape of the input to fulfil the physical constraints calculated on the output. With this procedure it is possible to get both a high precision of the predicted flow field and an interaction between the constraints and the geometrical shape.\\
\indent
It has to be mentioned that the STN requires a proper initialization. Therefore, the STN is pretrained to reproduce the input geometries from the training data set, which simply means to pass input through the STN without any transformation. This is important since otherwise the STN tends to diverge, because of strong transformation at the beginning of the training. Moreover it turns out that a learning rate of~$10^{-5}$ leads to the best optimization performance. With a small learning rate the shape is changing slightly so the STN can better react to changes in the flow field and hence in the loss function.
\subsection{Physical Constraints}
\begin{figure}[t]
\center
  \def\svgwidth{200pt}
  \input{BoundariesForces.pdf_tex}
\caption{Inlet and outlet boundary for calculating $\Delta p$ and the top and bottom surface of the airfoil used for the forces $F_i$ marked in black and magenta.}
\label{BoundariesForces}
\end{figure}
The overall goal of this work is the manipulation of input geometries with respect to physical equations, which are acting as constraints to the system. These equations are calculated from the values of the output flow field and are thus coupled to the input geometry via both networks. Two equations for constraining the optimization are presented. This includes the total pressure difference~$\Delta p$ between two boundaries
\begin{equation}
 \Delta p = \Big(\frac{\rho}{2} (|u_2+v_2|^2)+p_2\Big) - \Big(\frac{\rho}{2} (|u_1+v_1|^2)+p_1\Big)\;,
\end{equation}
with the velocities $u$, $v$, the pressure $p$ and the density of the fluid~$\rho$. The subscripts 1 and 2 denote the inlet and outlet boundaries between which $\Delta p$ is calculated, as shown in Figure~\ref{BoundariesForces}. For~$\Delta p$ the values $u$, $v$ and $p$ are averaged over the boundary area. Since all data are stored on a regular grid, the functions are evaluated on a discrete domain, i.e. per pixel. For example the velocity~$u_n$ used for $\Delta p$ is simply the $n$-th column in the data matrix of the channel which corresponds to the~$u$-values.
\\
\indent
Also the pressure forces~$F_i$ on the object surface are used as constraints for the shape optimization
\begin{equation}
 F_i = \int_{A_i} p_i\;dA_i\;,
\end{equation}
where~$A_i$, $i=1,\ldots,4$ represents the front, back, top and bottom surface and $p_i$ the pressure. Figure \ref{BoundariesForces} displays an example of the pixels used for the top and bottom surface, marked in black and magenta. In the discrete domain the integral of the force~$F_i$ can be written as a sum over all pressure values of the pixels belonging to the surface of the geometry. Since the surface~$A_i$ is constructed from a set of pixels with a constant edge length, this is simply multiplying the pressure~$p_i$ for every pixel by the edge length of the pixel.
\\
\indent
The total loss for the shape optimization is then given as
\begin{equation}
 \mathcal{L}_{\mathrm{total}} = (\Delta \hat{p} - \Delta p)^2 + \sum_{i=1}^4 (\hat{F}_i - F_i)^2\;.
\end{equation}
The true values~$\Delta p$ and~$F_i$ are calculated on the flow field for a reference geometry to which we want to optimize the shape. Indeed, many other functions can be calculated on the flow field and be used as loss function, depending on how the physical system should be restricted. We further show this by using the length~$L$, height~$H$ and centre of mass~$COM$ of the object as additional criterions for the optimization.
\pgfplotsset{compat=1.5,
	every tick label/.append style={font=\scriptsize},
	legend image code/.code={\draw[mark repeat=1,mark phase=1] plot coordinates {(0cm,0cm)(0.0cm,0cm)(0.1cm,0cm)};},
}
\begin{figure}[!t]

	\begin{tabular}{cc}
		\begin{tikzpicture}
		\begin{axis}[
		width=135pt,
		height=100pt,

		xlabel={\scriptsize Channel Length},
		ylabel={\scriptsize Relative Error [\%]},
		xmin=0,
		xmax=255,
		ymin=0,
		ymax=8.5,
		legend pos=north west,
		grid=major,
		]
		\addplot[color=blue] table {relativErrors_u.txt};
		\addplot[color=red] table {relativErrors_v.txt};
		\addplot[color=green] table {relativErrors_p.txt};
		\addlegendentry{\scriptsize $u$}
		\addlegendentry{\scriptsize $v$}
		\addlegendentry{\scriptsize $p$}
		\end{axis}
		\end{tikzpicture}

		&

		\begin{tikzpicture}
		\begin{axis}[
		width=135pt,
		height=100pt,

		xlabel={\scriptsize Channel Length},
		ylabel={\scriptsize Relative Error [\%]},
		xmin=0,
		xmax=255,
		ymin=0,
		ymax=8.5,
		legend pos=north west,
		grid=major,
		]
		\addplot[color=blue] table {relativErrors_mass.txt};
		\addplot[color=red] table {relativErrors_energy.txt};
		\addlegendentry{\scriptsize $\Delta Q$}
		\addlegendentry{\scriptsize $\Delta p$}
		\end{axis}
		\end{tikzpicture}
	\end{tabular}
	\caption{Distribution of the mean relative error along the channel length. \textit{Left}: Error in $u$, $v$ and $p$. \textit{Right}: Error in $\Delta Q$ and $\Delta p$.}
	\label{relativeErrors}
\end{figure}
\begin{figure*}[t]
	\center

	\begin{tabular}{ccccc}
		\includegraphics[width=20mm]{img/geos_transformed_sharp/circle.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_asym_dp.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_asym_dpCOM.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_asym_SSE.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/asym.eps}\\

		\includegraphics[width=20mm]{img/geos_transformed_sharp/circle.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_sym_dp.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_sym_dpCOM.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_sym_SSE.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/sym.eps}\\

		\includegraphics[width=20mm]{img/geos_transformed_sharp/circle.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_symRot_dp.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_symRot_dpCOM.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_symRot_SSE.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/asymRot.eps}\\

		\includegraphics[width=20mm]{img/geos_transformed_sharp/tri.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_rect_dp.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_rect_dpCOM.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_rect_SSE.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/rect.eps}\\

		\includegraphics[width=20mm]{img/geos_transformed_sharp/rect.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_tri_dp.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_tri_dpCOM.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/airfoil_tri_SSE.eps} &
		\includegraphics[width=20mm]{img/geos_transformed_sharp/tri.eps}\\
		(a) Initial & (b) $\Delta p$, $F_i$ & (c) $\Delta p$, $F_i$, $L$ & (d) SSE & (e) Target\\
		& & \;\;\;\; $H$, $COM$ & &
	\end{tabular}

	\vspace{-0.2\baselineskip}
	\caption{Results of the shape transformation for the test cases with different constraints. (a) Initial geometry. (b) Total pressure difference $\Delta p$ and object forces $F_i$ constrained. (c) $\Delta p$ and $F_i$ with additional geometric restrictions. (d) All flow values $u$, $v$ and $p$ via $\mathcal{L}_{SSE}$. (e) Target geometry.}
	\label{resultsTrafo}
\end{figure*}
\section{Results}
To show the strong performance of the proposed method for the flow field prediction we use a dataset which has a high variance in terms of fluid mechanical properties and is more complex in comparison to those presented in related works. We show, that the shape optimization can be successfully applied to test cases with generic objects like rectangles or triangles. Further, we extend the experiments to real applications, such as the design of different airfoils. The design is optimized based on well known physical quantities which are typically used to analyse airfoils and are of relevance for the design of fluid machinery. Even for real applications we can achieve a good performance while keeping the flexibility of our model. Thus, we outperform other existing inverse design systems.
\subsection{Predicted Flow Fields}
\begin{table}[t]
	\center
	\caption{Relative error of $\Delta p$ and $F_i$ for the test cases with different constraints.}
	\label{resultsTable}
	\begin{tabular}{lccc}
		\hline
		\multicolumn{1}{c}{Target} & $\Delta p, F_i$ & $\Delta p, F_i, L, H, COM$ & SSE \\
		\hline\hline

		Airfoil (asym.) & 0.4\% & 0.01\%& 0.8\%\\
		\hline
		Airfoil (sym.) & 11.9\% & 1.1\% & 2.6\%\\
		\hline
		Airfoil (adjust.) & 0.7\% & 0.11\%& 0.14\%\\
		\hline
		Rectangle & 3.3\% & 0.06\% & 0.75\%\\
		\hline
		Triangle & 131\%& 0.8\% & 1.56\%\\
		\hline
	\end{tabular}
\end{table}
Since the shape transformation relies on the predicted flow field, the prediction of these values is a major issue in this method and a high accuracy is required. In this section a detailed analysis of the predicted flow fields is presented. We have 300 CFD-simulated flow fields as ground truth for the evaluation, which were not seen during training. First the accuracy over the whole flow field is presented. The mean relative error (MRE) of the normalized quantities is used for evaluation, since it yields an error percentage for the predicted solution. The reference value for the velocity channels~$u,v$ is the averaged inflow velocity. For the pressure channel~$p$ the averaged pressure at the outlet is used. These reference values are chosen since the inlet velocities and the outlet pressure are also used as boundary conditions for the CFD-simulation. The errors are not equally distributed over the three channels, which yield relative errors of 4.34\% for the $x$-velocity channel, 2.5\% for the $y$-velocity and 1.88\% for the pressure. Especially the pressure values have a small error, which is useful since the pressure forces~$F_i$ used for the shape optimization only depend on the pressure values.\\
\indent
Further the distribution of the MRE in $u,v$~and~$p$ along the channel length is analysed. The channel length is represented by 256 pixels along the $x$-direction and the MRE is calculated per column of the associated channel of the data matrix. The results are shown in Figure~\ref{relativeErrors} (left). The velocities in the middle part of the channel and downstream are varying more than the velocities at the inlet because of the objects, which are diverting the flow. This results in increasing errors of the predicted velocities along the channel length. In contrast, stagnation points in front of the objects result in larger pressure gradients in the front part of the channel and thus in decreasing errors of the predicted pressure values over the length.\\
\indent
Since the interest is in physical quantities calculated on the flow field, the continuity equation $\Delta Q$ and the total pressure difference $\Delta p$ are analysed. The continuity equation is given as
\begin{equation}
 \Delta Q = \rho u_2 A_2 - \rho u_1 A_1\;,
\end{equation}
with density~$\rho$ and $A_{1,2}$ denoting the inlet and outlet surface, respectively. The velocity $u$ is again averaged over the cross-sectional area of the channel. The inlet position is fixed to the first column of the data matrix. The outlet position is shifted stepwise over the channel length. The MRE is also used here to analyse $\Delta Q$ and $\Delta p$ normalized to the mass flow \mbox{$Q_1=\rho u_1 A_1$} and the energy term $\big(\frac{\rho}{2} (|u_1+v_1|^2)+p_1\big)$ at the inlet, respectively. From Figure \ref{relativeErrors} (right) it is visible that the error of $\Delta Q$ is staying below 2\%. Also the error in $\Delta p$ is low for broad areas of the channel. This is important since $\Delta p$ is further used in the loss function $\mathcal{L}_{total}$ for the shape optimization.
\subsection{Transformed Geometries}
\begin{figure}[t]
\center
\begin{tabular}{cc}
	\includegraphics[width=40mm]{img/u_airfoil_asym_trafo_pred.eps}&\includegraphics[width=40mm]{img/u_airfoil_rot_trafo_pred}\\
	\includegraphics[width=40mm]{img/u_airfoil_asym_trafo_cfd.eps}&\includegraphics[width=40mm]{img/u_airfoil_rot_trafo_cfd}\\
	\includegraphics[width=40mm]{img/u_airfoil_asym_true_cfd.eps}&\includegraphics[width=40mm]{img/u_airfoil_rot_true_cfd}
\end{tabular}
\caption{Validation of the transformed geometry. \textit{Top}: Predicted values $u$. \textit{Middle}: CFD-simulated values $u$. \textit{Bottom}: CFD-simulation of the target.}
\label{comparisonPredCFD}
\end{figure}
The previous shown results give a solid basis for the following shape transformation. We will present three configurations with different physical constraints. First the total pressure difference $\Delta p$ and the object forces $F_i$ will be used as constraints. Second, additional the object length $L$, height~$H$ and the centre of mass $COM$ will be restricted to match the target geometry. For the last configuration all values of~($u$,~$v$,~$p$) over the whole field will be used as constraints for the transformation via the $\mathcal{L}_{SSE}$. This configuration is used to show the maximum potential of the proposed transformation method.\\
\indent
For every configuration different initial and target geometries are used. This includes generic objects such as a circle, rectangle and triangle, and more realistic objects such as a symmetric and an asymmetric airfoil, and a airfoil with an adjusted angle. This leads to 15 different test cases. The columns (a) and (e) in Figure \ref{resultsTrafo} are showing the used initial geometries and the respective target geometries. The flow field of the target geometries is used to calculate the physical quantities which are used as target values for the geometry transformation, i.e. ground truth.
Table \ref{resultsTable} shows the relative error between the ground truth and the physical quantities calculated on the estimated flow field resulting from the transformed geometry. For all the test cases only the mean relative error of $\Delta p$ and $F_i$ is shown for being able to compare the influence of the different constraints.\\
\indent
From Figure \ref{resultsTrafo} (b) it is visible that restricting $\Delta p$ and $F_i$ yields to transformed objects which are somehow looking like the target objects. Especially the asymmetric airfoil in the first row and the airfoil with adjusted angle in the third row have high similarities to their target objects. However, by using only $\Delta p$ and $F_i$ as constraints the solution space is broad. Thus, many objects with different shapes can fulfil these constraints. For example a symmetric airfoil as shown in the second row has equal forces on the top and bottom surface. It is visible that also the transformed airfoil has a symmetric shape. The relative error in Table \ref{resultsTable} is showing that the parameters of the transformed symmetric airfoil are close to these of the target airfoil. Only the triangle could not be transformed successfully. The sharp corner at the front of the triangle is leading to strong varying pressure distributions at this point even for small geometric variations. Thus, the system is not able to converge to a proper solution, since the loss function is dominated by the pressure distribution.\\
\indent
With additional constraints for the object length $L$, height~$H$ and the centre of mass $COM$ the solution space is getting small. This has a large impact to the transformation leading to results which are similar to the target shape. This is valid for all examples as shown in Figure \ref{resultsTrafo} (c). However the generic objects have more difficulties during the transformation, since the sharp corners are still causing strong varying pressure distributions. Also the relative error of $\Delta p$ and $F_i$ is decreasing for all examples to values smaller than $1.1\%$ which is showing the power of these physical constraints for transforming the objects.\\
\indent
To further analyse the maximum potential of the transformation all values of $u$, $v$ and $p$ over the whole field are used as constraints via the $\mathcal{L}_{SSE}$ which is indeed a strong restriction. Also the flow field of a target geometry is in general not known in a real world application. Nevertheless this process is used to show that it is possible to match the target shape with the proposed transformation method. The results are presented in Figure \ref{resultsTrafo} (d). Only the rectangle has a curved edge at the backside.
Since the $\mathcal{L}_{SSE}$ is taking all values of $u$, $v$ and $p$ into account, the prediction near the edges of the objects is getting slightly worse. Thus, the relative error of $\Delta p$ and $F_i$ is increasing compared to the former loss function.
\\
\indent
To validate the performance of the shape optimization, CFD-simulations are done for the transformed geometries with FEniCS. Figure \ref{comparisonPredCFD} presents the velocity component $u$ of two different airfoils for the case where $\Delta p$, $F_i$
and geometric restrictions are used as constraints. The first row displays the predicted values of the U-Net for the transformed geometries. The second row displays the values of the CFD-simulation of the same transformed geometries. It is visible that the predicted values are close to the values from the CFD-simulation. As a comparison the CFD-simulation of the target geometry is revealed in the last row. The values from the transformed geometries are similar to the CFD-simulated values of the target geometry. This is showing that the presented method is able to find a solution which is fulfilling the physical constraints

\section{Conclusion}
The proposed method demonstrates how objects can be transformed subject to varying physical constraints, thus providing a flexible and transferable model to a wide variety of problem setups. Beside the presented results concerning flow field prediction, this method can be applied to any kind of data representing vector fields, like electromagnetic fields or forces and stress values in a mechanical system. Further this method can also be applied to other tasks that aim to estimate parameters of objects. The next step is to apply the model to complex real applications and extend it to 3D data.

\bibliographystyle{IEEEtran}

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