text style changes
Browse files
    	
        app.py
    CHANGED
    
    | @@ -97,9 +97,9 @@ css = """ | |
| 97 | 
             
            with gr.Blocks(css=css) as demo:
         | 
| 98 | 
             
                gr.Markdown(
         | 
| 99 | 
             
                    """
         | 
| 100 | 
            -
                    #  | 
| 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 | 
            -
                    ##  | 
| 161 | 
            -
                    ###  | 
| 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 | 
            -
                    ###  | 
| 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 | 
            -
                    ###  | 
| 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 | 
            -
                    ###  | 
| 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 | 
            -
                    ###  | 
| 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 | 
            -
                    ##  | 
| 179 | 
            -
                    Traditional PDE solvers are computationally expensive  | 
| 180 |  | 
| 181 | 
            -
                     | 
| 182 | 
            -
                     | 
| 183 | 
            -
                     | 
| 184 |  | 
| 185 | 
            -
                    It's a step towards universal scientific models, just like foundation models transformed NLP and vision. | 
| 186 |  | 
| 187 | 
             
                    ---
         | 
| 188 |  | 
| 189 | 
            -
                    ##  | 
| 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 | 
            -
                     | 
| 194 | 
            -
                     | 
| 195 | 
            -
                     | 
| 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 |  | 
