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--- |
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datasets: polymathic-ai/viscoelastic_instability |
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tags: |
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- physics |
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--- |
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# 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. |
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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. |
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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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# Fourier Neural Operator |
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Implementation of the [Fourier Neural Operator](https://arxiv.org/abs/2010.08895) provided by [`neuraloperator v0.3.0`](https://neuraloperator.github.io/dev/index.html). |
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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 | |
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|-------------|--------| |
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| Modes | 16 | |
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| Blocks | 4 | |
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| Hidden Size | 128 | |
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## Trained Model Versions |
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Below is the list of checkpoints available for the training of FNO on different datasets of the Well. |
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| Dataset | Best Learning Rate | Epochs | VRMSE | |
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|----------------------------------------|--------------------|--------|--------| |
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| [acoustic_scattering_maze](https://huggingface.co/polymathic-ai/FNO-acoustic_scattering_maze) | 1E-3 | 27 | 0.5033 | |
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| [active_matter](https://huggingface.co/polymathic-ai/FNO-active_matter) | 5E-3 | 239 | 0.3157 | |
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| [convective_envelope_rsg](https://huggingface.co/polymathic-ai/FNO-convective_envelope_rsg) | 1E-4 | 14 | 0.0224 | |
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| [gray_scott_reaction_diffusion](https://huggingface.co/polymathic-ai/FNO-gray_scott_reaction_diffusion) | 1E-3 | 46 | 0.2044 | |
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| [helmholtz_staircase](https://huggingface.co/polymathic-ai/FNO-helmholtz_staircase) | 5E-4 | 132 | 0.00160| |
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| [MHD_64](https://huggingface.co/polymathic-ai/FNO-MHD_64) | 5E-3 | 170 | 0.3352 | |
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| [planetswe](https://huggingface.co/polymathic-ai/FNO-planetswe) | 5E-4 | 49 | 0.0855 | |
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| [post_neutron_star_merger](https://huggingface.co/polymathic-ai/FNO-post_neutron_star_merger) | 5E-4 | 104 | 0.4144 | |
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| [rayleigh_benard](https://huggingface.co/polymathic-ai/FNO-rayleigh_benard) | 1E-4 | 32 | 0.6049 | |
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| [rayleigh_taylor_instability](https://huggingface.co/polymathic-ai/FNO-rayleigh_taylor_instability) | 5E-3 | 177 | 0.4013 | |
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| [shear_flow](https://huggingface.co/polymathic-ai/FNO-shear_flow) | 1E-3 | 24 | 0.4450 | |
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| [supernova_explosion_64](https://huggingface.co/polymathic-ai/FNO-supernova_explosion_64) | 1E-4 | 40 | 0.3804 | |
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| [turbulence_gravity_cooling](https://huggingface.co/polymathic-ai/FNO-turbulence_gravity_cooling) | 1E-4 | 13 | 0.2381 | |
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| [turbulent_radiative_layer_2D](https://huggingface.co/polymathic-ai/FNO-turbulent_radiative_layer_2D) | 5E-3 | 500 | 0.4906 | |
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| [viscoelastic_instability](https://huggingface.co/polymathic-ai/FNO-viscoelastic_instability) | 5E-3 | 205 | 0.7195 | |
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## Loading the model from Hugging Face |
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To load the FNO model trained on the `viscoelastic_instability` of the Well, use the following commands. |
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```python |
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from the_well.benchmark.models import FNO |
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model = FNO.from_pretrained("polymathic-ai/FNO-viscoelastic_instability") |
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``` |
