polymathic-ai/FNO-active_matter

Benchmarking Models on the Well

The Well is a 15TB dataset collection of physics simulations. This model is part of the models that have been benchmarked on the Well.

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.

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.

Fourier Neural Operator

Implementation of the Fourier Neural Operator provided by neuraloperator v0.3.0.

Model Details

For benchmarking on the Well, we used the following parameters.

Parameters	Values
Modes	16
Blocks	4
Hidden Size	128

Trained Model Versions

Below is the list of checkpoints available for the training of FNO on different datasets of the Well.

Dataset	Best Learning Rate	Epochs	VRMSE
acoustic_scattering_maze	1E-3	27	0.5033
active_matter	5E-3	239	0.3157
convective_envelope_rsg	1E-4	14	0.0224
gray_scott_reaction_diffusion	1E-3	46	0.2044
helmholtz_staircase	5E-4	132	0.00160
MHD_64	5E-3	170	0.3352
planetswe	5E-4	49	0.0855
post_neutron_star_merger	5E-4	104	0.4144
rayleigh_benard	1E-4	32	0.6049
rayleigh_taylor_instability	5E-3	177	0.4013
shear_flow	1E-3	24	0.4450
supernova_explosion_64	1E-4	40	0.3804
turbulence_gravity_cooling	1E-4	13	0.2381
turbulent_radiative_layer_2D	5E-3	500	0.4906
viscoelastic_instability	5E-3	205	0.7195

Loading the model from Hugging Face

To load the FNO model trained on the active_matter of the Well, use the following commands.

from the_well.benchmark.models import FNO

model = FNO.from_pretrained("polymathic-ai/FNO-active_matter")