cgeorgiaw HF Staff commited on
Commit
278bc47
·
1 Parent(s): 021f219

text style changes

Browse files
Files changed (1) hide show
  1. app.py +22 -23
app.py CHANGED
@@ -97,9 +97,9 @@ css = """
97
  with gr.Blocks(css=css) as demo:
98
  gr.Markdown(
99
  """
100
- # 🚀 POSEIDON: Foundation Models for PDEs 🌊🔬
101
 
102
- POSEIDON is a **foundation model** for solving **Partial Differential Equations (PDEs)** efficiently. Instead of training a separate model for each PDE, POSEIDON **learns a general solution operator**—allowing it to **generalize across different physics** with minimal data. Think of it as the **GPT-4 for PDEs**, trained on a diverse set of **fluid dynamics equations** and capable of adapting to **new, unseen physical systems**. 🌍⚡
103
 
104
  # **Dataset Explorer**
105
  POSEIDON provides solutions to a variety of fluid dynamics problems. Below are a few datasets you can explore:
@@ -116,7 +116,7 @@ with gr.Blocks(css=css) as demo:
116
  - Models shock interactions across uncertain boundaries, crucial for hypersonic flows and uncertainty quantification.
117
  - Helps in high-speed aerodynamics and robust PDE solvers.
118
 
119
- Explore these datasets to visualize fluid behavior and analyze dynamic flow evolution! 🚀
120
  """
121
  )
122
 
@@ -157,44 +157,44 @@ with gr.Blocks(css=css) as demo:
157
 
158
  gr.Markdown(
159
  """
160
- ## 🔥 Key Innovations
161
- ### 🔹 **Multiscale Operator Transformer (scOT) 🧠**
162
  A hierarchical transformer-based architecture that captures PDE solution dynamics across multiple spatial and temporal scales. It uses shifted-window attention (SwinV2) to efficiently process large solution spaces.
163
 
164
- ### 🔹 **Continuous-in-Time Learning ⏳**
165
  Instead of learning PDE solutions at discrete time steps, POSEIDON uses time-conditioned layer normalization, enabling predictions at **any arbitrary time**—like a **true continuous function**.
166
 
167
- ### 🔹 **All2All Training Strategy 📈**
168
  By leveraging the semi-group property of PDEs, POSEIDON scales training data quadratically without additional simulations. Every time step becomes a learning opportunity!
169
 
170
- ### 🔹 **Pretrained on Fluid Dynamics, Generalizes to New Physics 🌊**
171
- Trained on compressible Euler and Navier-Stokes equations, POSEIDON transfers its knowledge to unseen wave, diffusion, and reaction-diffusion PDEs—a huge step for scientific machine learning! 💡
172
 
173
- ### 🔹 **Outperforms FNO & Neural Operators 🚀**
174
- POSEIDON achieves the same accuracy as an FNO trained on 1024 samples—using only 20 samples. That's a 50x efficiency boost in sample efficiency. 📉
175
 
176
  ---
177
 
178
- ## 🎯 Why Does This Matter?
179
- Traditional PDE solvers are computationally expensive 🖥️💰. POSEIDON is a general-purpose neural PDE solver that:
180
 
181
- Works across multiple physics domains
182
- Requires fewer training samples
183
- Enables real-time simulation & forecasting
184
 
185
- It's a step towards universal scientific models, just like foundation models transformed NLP and vision. 🚀
186
 
187
  ---
188
 
189
- ## 🌟 Try POSEIDON Now!
190
 
191
  You can experiment and empower your research with POSEIDON-T (21M parameters), POSEIDON-B (158M parameters), and POSEIDON-L (629M parameters).
192
 
193
- 🔗 **Pretrained models & datasets**: [Hugging Face Hub](https://huggingface.co/camlab-ethz)
194
- 📜 **Code & Paper**: [GitHub](https://github.com/camlab-ethz/poseidon) | [arXiv](https://arxiv.org/abs/2405.19101)
195
- 💬 **Join the Discussion**: [Hugging Face Forums](https://discuss.huggingface.co/)
196
 
197
- Let's reshape the future of PDE solving—one foundation model at a time! 🚀🔬
198
 
199
  ---
200
 
@@ -209,7 +209,6 @@ with gr.Blocks(css=css) as demo:
209
  primaryClass={cs.LG}
210
  }
211
  ```
212
-
213
  """
214
  )
215
 
 
97
  with gr.Blocks(css=css) as demo:
98
  gr.Markdown(
99
  """
100
+ # POSEIDON: Foundation Models for PDEs 🌊🔬
101
 
102
+ POSEIDON is a **foundation model** for solving **Partial Differential Equations (PDEs)** efficiently. Instead of training a separate model for each PDE, POSEIDON **learns a general solution operator**—allowing it to **generalize across different physics** with minimal data. Think of it as the **GPT-4 for PDEs**, trained on a diverse set of **fluid dynamics equations** and capable of adapting to **new, unseen physical systems**.
103
 
104
  # **Dataset Explorer**
105
  POSEIDON provides solutions to a variety of fluid dynamics problems. Below are a few datasets you can explore:
 
116
  - Models shock interactions across uncertain boundaries, crucial for hypersonic flows and uncertainty quantification.
117
  - Helps in high-speed aerodynamics and robust PDE solvers.
118
 
119
+ Explore these datasets to visualize fluid behavior and analyze dynamic flow evolution!
120
  """
121
  )
122
 
 
157
 
158
  gr.Markdown(
159
  """
160
+ ## Key Innovations
161
+ ### **Multiscale Operator Transformer (scOT)**
162
  A hierarchical transformer-based architecture that captures PDE solution dynamics across multiple spatial and temporal scales. It uses shifted-window attention (SwinV2) to efficiently process large solution spaces.
163
 
164
+ ### **Continuous-in-Time Learning**
165
  Instead of learning PDE solutions at discrete time steps, POSEIDON uses time-conditioned layer normalization, enabling predictions at **any arbitrary time**—like a **true continuous function**.
166
 
167
+ ### **All2All Training Strategy**
168
  By leveraging the semi-group property of PDEs, POSEIDON scales training data quadratically without additional simulations. Every time step becomes a learning opportunity!
169
 
170
+ ### **Pretrained on Fluid Dynamics, Generalizes to New Physics**
171
+ Trained on compressible Euler and Navier-Stokes equations, POSEIDON transfers its knowledge to unseen wave, diffusion, and reaction-diffusion PDEs—a huge step for scientific machine learning!
172
 
173
+ ### **Outperforms FNO & Neural Operators**
174
+ POSEIDON achieves the same accuracy as an FNO trained on 1024 samples—using only 20 samples. That's a 50x efficiency boost in sample efficiency.
175
 
176
  ---
177
 
178
+ ## Why Does This Matter?
179
+ Traditional PDE solvers are computationally expensive. POSEIDON is a general-purpose neural PDE solver that:
180
 
181
+ Works across multiple physics domains
182
+ Requires fewer training samples
183
+ Enables real-time simulation & forecasting
184
 
185
+ It's a step towards universal scientific models, just like foundation models transformed NLP and vision.
186
 
187
  ---
188
 
189
+ ## Try POSEIDON Now!
190
 
191
  You can experiment and empower your research with POSEIDON-T (21M parameters), POSEIDON-B (158M parameters), and POSEIDON-L (629M parameters).
192
 
193
+ **Pretrained models & datasets**: [Hugging Face Hub](https://huggingface.co/camlab-ethz)
194
+ **Code & Paper**: [GitHub](https://github.com/camlab-ethz/poseidon) | [arXiv](https://arxiv.org/abs/2405.19101)
195
+ **Join the Discussion**: [Hugging Face Forums](https://discuss.huggingface.co/)
196
 
197
+ Let's reshape the future of PDE solving—one foundation model at a time!
198
 
199
  ---
200
 
 
209
  primaryClass={cs.LG}
210
  }
211
  ```
 
212
  """
213
  )
214