| --- |
| datasets: polymathic-ai/gray_scott_reaction_diffusion |
| tags: |
| - physics |
| --- |
| |
| # Benchmarking Models on the Well |
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| [The Well](https://github.com/PolymathicAI/the_well) is a 15TB dataset collection of physics simulations. This model is part of the models that have been benchmarked on the Well. |
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| The models have been trained for a fixed time of 12 hours or up to 500 epochs, whichever happens first. The training was performed on a NVIDIA H100 96GB GPU. |
| In the time dimension, the context length was set to 4. The batch size was set to maximize the memory usage. We experiment with 5 different learning rates for each model on each dataset. |
| We use the model performing best on the validation set to report test set results. |
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| The reported results are here to provide a simple baseline. **They should not be considered as state-of-the-art**. We hope that the community will build upon these results to develop better architectures for PDE surrogate modeling. |
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| # U-Net |
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| Implementation of the [U-Net model](https://arxiv.org/abs/1505.04597). |
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| ## Model Details |
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| For benchmarking on the Well, we used the following parameters. |
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| | Parameters | Values | |
| |---------------------|--------| |
| | Spatial Filter Size | 3 | |
| | Initial Dimension | 48 | |
| | Block per Stage | 1 | |
| | Up/Down Blocks | 4 | |
| | Bottleneck Blocks | 1 | |
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| ## Trained Model Versions |
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| Below is the list of checkpoints available for the training of U-Net on different datasets of the Well. |
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| | Dataset | Learning Rate | Epochs | VRMSE | |
| |---------|---------------|--------|-------| |
| | [acoustic_scattering_maze](https://huggingface.co/polymathic-ai/UNETClassic-acoustic_scattering_maze) | 1E-2 | 26 | 0.0395 | |
| | [active_matter](https://huggingface.co/polymathic-ai/UNETClassic-active_matter) | 5E-3 | 239 | 0.2609 | |
| | [convective_envelope_rsg](https://huggingface.co/polymathic-ai/UNETClassic-convective_envelope_rsg) | 5E-4 | 19 | 0.0701 | |
| | [gray_scott_reaction_diffusion](https://huggingface.co/polymathic-ai/UNETClassic-gray_scott_reaction_diffusion) | 1E-2 | 44 | 0.5870 | |
| | [helmholtz_staircase](https://huggingface.co/polymathic-ai/UNETClassic-helmholtz_staircase) | 1E-3 | 120 | 0.01655 | |
| | [MHD_64](https://huggingface.co/polymathic-ai/UNETClassic-MHD_64) | 5E-4 | 165 | 0.1988 | |
| | [planetswe](https://huggingface.co/polymathic-ai/UNETClassic-planetswe) | 1E-2 | 49 | 0.3498 | |
| | post_neutron_star_merger | - | - | – | |
| | [rayleigh_benard](https://huggingface.co/polymathic-ai/UNETClassic-rayleigh_benard) | 1E-4 | 29 | 0.8448 | |
| | [rayleigh_taylor_instability](https://huggingface.co/polymathic-ai/UNETClassic-rayleigh_taylor_instability) | 5E-4 | 193 | 0.6140 | |
| | [shear_flow](https://huggingface.co/polymathic-ai/UNETClassic-shear_flow) | 5E-4 | 29 | 0.836 | |
| | [supernova_explosion_64](https://huggingface.co/polymathic-ai/UNETClassic-supernova_explosion_64) | 5E-4 | 46 | 0.3242 | |
| | [turbulence_gravity_cooling](https://huggingface.co/polymathic-ai/UNETClassic-turbulence_gravity_cooling) | 1E-3 | 14 | 0.3152 | |
| | [turbulent_radiative_layer_2D](https://huggingface.co/polymathic-ai/UNETClassic-turbulent_radiative_layer_2D) | 5E-3 | 500 | 0.2394 | |
| | [viscoelastic_instability](https://huggingface.co/polymathic-ai/UNETClassic-viscoelastic_instability) | 5E-4 | 198 | 0.3147 | |
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| ## Loading the model from Hugging Face |
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| To load the UNetClassic model trained on the `gray_scott_reaction_diffusion` of the Well, use the following commands. |
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|
| ```python |
| from the_well.benchmark.models import UNetClassic |
| |
| model = UNetClassic.from_pretrained("polymathic-ai/UNetClassic-gray_scott_reaction_diffusion") |
| ``` |
