Answers.Body: <p>You might want to try <a href="https://en.wikipedia.org/wiki/Symbolic_regression" rel="nofollow noreferrer">symbolic regression</a>. This is a machine learning approach that tries to generate an equation with arbitrary form that best fits a set of examples. I've used it before when working with physicists who wanted an equation in terms of known numeric constants and specific variables, but didn't expect the equation to be linear or one of the other shapes for which we have standard regression models.</p>
  
  <p>Symbolic regression often (usually?) uses <a href="https://deap.readthedocs.io/en/0.7-0/examples/symbreg.html" rel="nofollow noreferrer">genetic programming</a> for the underlying optimization. A decent tool is <a href="https://www.nutonian.com/products/eureqa/" rel="nofollow noreferrer">Eureka</a>. It used to be free, but I think they want a payment now. You can also do it yourself from any genetic programming toolkit with a little know-how.   </p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2018-08-08T15:46:28.823Z
Answers.LastActivityDate: 2018-08-08T15:46:28.823Z
Answers.UserDisplayName: John Doucette
Body: <p>I'm trying to design an orbital rendezvous program for Kerbal Space Program.  I'm focusing on when to launch my spacecraft so that I can end up in the general vicinity of the target.  If I can control the ascent profile, the remaining dependent variables are the ship's twr and the target's altitude.  I want to try a computer learning solution.</p>
  
  <p>What is the best way to formulate the problem of learning the time to launch based on some twr?  </p>
  
  <p>How can I make an algorithm to compute the general equation of launch time to a altitude based on my ability to accelerate?  What type of learning problem could this be classified as?  What are some approaches to solve problems with known dependent variables?</p>
  
  <p>This may be an obvious question, I kind of expect the answer is regression?  But it seemed a general enough question to be sure about to get a solid foothold in computer learning with this type of problem, which seems to come up a lot.</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-03-11T12:35:57.113Z
Comments.Text: Question is how to calculate the trajectory of an object?
Comments.UserDisplayName: pasaba por aqui
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-03-11T17:33:14.067Z
Comments.Text: No, powered flight is involved.  Also the approach was NOT to calculate the trajectory of ONE (powered)object, but to have a learning algorithm take a good guess at the equation for time as a function of twr for ALL objects.
Comments.UserDisplayName: Oblivion
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-03-11T18:21:02.103Z
Comments.Text: Meaning of "twr" ? Not in my lost of acronyms
Comments.UserDisplayName: pasaba por aqui
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-03-11T18:27:00.113Z
Comments.Text: thrust to weight ratio.
Comments.UserDisplayName: Oblivion
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-03-11T18:29:24.823Z
Comments.Text: Could you post involved equations?
Comments.UserDisplayName: pasaba por aqui
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-03-11T22:29:07.173Z
Comments.Text: That's what I want to know.  Usually you have dependent variables, an equation and you solve to get independent variables.
  
  What I'm asking is if I have the dependent variables, and experimental independent variables, what is the best way to learn the equation?
Comments.UserDisplayName: Oblivion
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-03-12T01:15:05.537Z
Comments.Text: What you mean by "learning" is not clear, are you trying to optimize a process or find an optimum point of data which you can reuse?  or are you seeking a way to feed data into an AI object (ie NN) which will give more precision based on how much data it is given?
Comments.UserDisplayName: solarflare
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-03-19T16:32:27.627Z
Comments.Text: I would like the program find an equation or at least the coefficients of an equation that would correspond to the general case of the time to get to orbit.
Comments.UserDisplayName: Oblivion
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-03-19T16:36:57.107Z
Comments.Text: I'm not sure that I'll get an answer to this one,  but no one commenting seems to understand what I'm getting at.  I am more interested in a general solution at this point, but in terms of the variables already mentioned:
  
  You launch 5 spacecraft into space.  Each has different parameters.  You can control the ascent profile generally.  Each has a different time because there are different designs.
  
  The question I'd like to ask a program is what is the equation that best matches the various launches?
Comments.UserDisplayName: Oblivion
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-03-19T16:42:22.410Z
Comments.Text: Another way to put it is how much weight do each of the variables we know about matter.  For instance, how much does twr matter?  does it scale linearly?  Is it directly proportional to some other variable?  Another part of this is the unknown variables.  What is the nature of the unknown variables?   It is kind of a solver.  Once again, I know the variables, some experimental, some, like thrust is easily knowable.  How can i develop a system to analyze the remaining parts of the equation?
Comments.UserDisplayName: Oblivion
Tags: <machine-learning>
Title: How can I have a computer learn the equation with known dependent variables?
UserDisplayName: Oblivion
ThreadText: # How can I have a computer learn the equation with known dependent variables?
  
  (Asked by: username_0 on 2018-03-10)
  
  I'm trying to design an orbital rendezvous program for Kerbal Space Program. I'm focusing on when to launch my spacecraft so that I can end up in the general vicinity of the target. If I can control the ascent profile, the remaining dependent variables are the ship's twr and the target's altitude. I want to try a computer learning solution.
  
  What is the best way to formulate the problem of learning the time to launch based on some twr?
  
  How can I make an algorithm to compute the general equation of launch time to a altitude based on my ability to accelerate? What type of learning problem could this be classified as? What are some approaches to solve problems with known dependent variables?
  
  This may be an obvious question, I kind of expect the answer is regression? But it seemed a general enough question to be sure about to get a solid foothold in computer learning with this type of problem, which seems to come up a lot.
  
  **Tags:** machine-learning
  > **Comments:**
  > **username_1**: Question is how to calculate the trajectory of an object?  
  > **username_0**: No, powered flight is involved.  Also the approach was NOT to calculate the trajectory of ONE (powered)object, but to have a learning algorithm take a good guess at the equation for time as a function of twr for ALL objects.  
  > **username_1**: Meaning of "twr" ? Not in my lost of acronyms  
  > **username_0**: thrust to weight ratio.  
  > **username_1**: Could you post involved equations?  
  > **username_0**: That's what I want to know.  Usually you have dependent variables, an equation and you solve to get independent variables.  What I'm asking is if I have the dependent variables, and experimental independent variables, what is the best way to learn the equation?  
  > **username_2**: What you mean by "learning" is not clear, are you trying to optimize a process or find an optimum point of data which you can reuse?  or are you seeking a way to feed data into an AI object (ie NN) which will give more precision based on how much data it is given?  
  > **username_0**: I would like the program find an equation or at least the coefficients of an equation that would correspond to the general case of the time to get to orbit.  
  > **username_0**: I'm not sure that I'll get an answer to this one,  but no one commenting seems to understand what I'm getting at.  I am more interested in a general solution at this point, but in terms of the variables already mentioned:  You launch 5 spacecraft into space.  Each has different parameters.  You can control the ascent profile generally.  Each has a different time because there are different designs.  The question I'd like to ask a program is what is the equation that best matches the various launches?  
  > **username_0**: Another way to put it is how much weight do each of the variables we know about matter.  For instance, how much does twr matter?  does it scale linearly?  Is it directly proportional to some other variable?  Another part of this is the unknown variables.  What is the nature of the unknown variables?   It is kind of a solver.  Once again, I know the variables, some experimental, some, like thrust is easily knowable.  How can i develop a system to analyze the remaining parts of the equation?  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_3 on 2018-08-08. Score: 1
  
  You might want to try [symbolic regression](https://en.wikipedia.org/wiki/Symbolic_regression). This is a machine learning approach that tries to generate an equation with arbitrary form that best fits a set of examples. I've used it before when working with physicists who wanted an equation in terms of known numeric constants and specific variables, but didn't expect the equation to be linear or one of the other shapes for which we have standard regression models.
  
  Symbolic regression often (usually?) uses [genetic programming](https://deap.readthedocs.io/en/0.7-0/examples/symbreg.html) for the underlying optimization. A decent tool is [Eureka](https://www.nutonian.com/products/eureqa/). It used to be free, but I think they want a payment now. You can also do it yourself from any genetic programming toolkit with a little know-how.
  
  
  ---
  
  