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The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning
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Introduces The Well, a 15TB collection of 16 diverse spatiotemporal physics simulation datasets with a unified PyTorch benchmarking library and baseline surrogate models (FNO, TFNO, U-net, CNextU-net).
Problem
Deep learning surrogate models for physical dynamics are evaluated on small, narrow sets of simulations, making it hard to assess new approaches across diverse, complex physics at manageable scale.
Approach
A large, curated, standardized collection of diverse high-fidelity simulation datasets (HDF5 with shared spec) spanning fluids, acoustics, astrophysics, and biology, plus a unified PyTorch interface and time-boxed baseline benchmarks for autoregressive next-step and rollout prediction.
Key results
- CNextU-net achieves best one-step VRMSE on 8 of 17 experiments, e.g., active_matter 0.1034 vs 0.2489 for U-net.
- Spectral (FNO/TFNO) and U-net-type models each win on roughly half the tasks, suggesting no single architecture dominates.
- Rayleigh-Taylor instability (At=0.25) yields VRMSE above 10 for all baselines, indicating the datasets remain very challenging.
Surprising findings
- Spectral and U-net-type models split wins roughly evenly, with no clear explanation from boundary conditions.
- Losses sometimes decrease in later rollout windows, attributed to dissipative solutions becoming smoother.
Limitations
- Datasets focus on uniform grids at manageable resolution, mostly 2D, while real applications are often 3D and use complex meshes.
- Many simulations are under-resolved, adding numerical viscosity, which limits inverse parameter inference use.
- Baselines are naive off-the-shelf settings and not tuned for peak performance.
Experimental setup
Datasets: acoustic_scattering active_matter convective_envelope_rsg euler_multi_quadrants gray_scott_reaction_diffusion helmholtz_staircase MHD_64 MHD_256 planetswe post_neutron_star_merger rayleigh_benard rayleigh_taylor_instability
Benchmarks: The Well (one-step and multi-step rollout VRMSE)
Metrics: VRMSE NRMSE per-field VRMSE spectral binned RMSE
Baselines: FNO TFNO U-net CNextU-net
Builds on: Fourier Neural Operator Tucker-factorized FNO U-net ConvNeXt
Closest papers by meaning
- Space and time continuous physics simulation from partial observations (ICLR 2024 · similarity 0.86)
- Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics (ICML 2024 · similarity 0.85)
- Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators (NeurIPS 2024 · similarity 0.84)
- Metamizer: A Versatile Neural Optimizer for Fast and Accurate Physics Simulations (ICLR 2025 · similarity 0.84)
- Parametric model reduction of mean-field and stochastic systems via higher-order action matching (NeurIPS 2024 · similarity 0.84)
- PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs (NeurIPS 2024 · similarity 0.84)
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