mlsanityData to 7 Oct 2026

The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning

arXiv 2412.00568 ↗First posted 30 Nov 2024cs.LG physics.flu-dyncited by 134

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Abstract (arXiv)

Machine learning based surrogate models offer researchers powerful tools for accelerating simulation-based workflows. However, as standard datasets in this space often cover small classes of physical behavior, it can be difficult to evaluate the efficacy of new approaches. To address this gap, we introduce the Well: a large-scale collection of datasets containing numerical simulations of a wide variety of spatiotemporal physical systems. The Well draws from domain experts and numerical software developers to provide 15TB of data across 16 datasets covering diverse domains such as biological systems, fluid dynamics, acoustic scattering, as well as magneto-hydrodynamic simulations of extra-galactic fluids or supernova explosions. These datasets can be used individually or as part of a broader benchmark suite. To facilitate usage of the Well, we provide a unified PyTorch interface for training and evaluating models. We demonstrate the function of this library by introducing example baselines that highlight the new challenges posed by the complex dynamics of the Well. The code and data is available at https://github.com/PolymathicAI/the_well.

Key facts. Cited by 134 papers in the map (data through 7 Oct 2026). Builds on 42 of its 216 references that are in the map. First posted on arXiv 30 Nov 2024.

Builds on

42 of 216 references.

References · 42

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 60; 2026: 73.

134 papers.

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  1. 2025EXP-Bench: Can AI Conduct AI Research Experiments?cited by 36
  2. 2025PDE-Transformer: Efficient and Versatile Transformers for Physics Simulationscited by 29
  3. 2025Generative Latent Neural PDE Solver using Flow Matchingcited by 28
  4. 2025Walrus: A Cross-Domain Foundation Model for Continuum Dynamicscited by 26
  5. 2025Reduced Order Modeling with Shallow Recurrent Decoder Networkscited by 24
  6. 2025DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic predictioncited by 21
  7. 2025PhysiX: A Foundation Model for Physics Simulationscited by 21
  8. 2025FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modelingcited by 19
  9. 2025Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulationcited by 19
  10. 2025Defining Foundation Models for Computational Science: A Call for Clarity and Rigorcited by 16
  11. 2026RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Datacited by 13
  12. 2025MORPH: PDE Foundation Models with Arbitrary Data Modalitycited by 12
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  2. 2024Predicting Change, Not States: An Alternate Framework for Neural PDE Surrogatescited by 8
  3. 2025FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modelingcited by 8
  4. 2026Test-time Generalization for Physics through Neural Operator Splittingcited by 8
  5. 2025TANTE: Time-Adaptive Operator Learning via Neural Taylor Expansioncited by 7
  6. 2025Towards autonomous quantum physics research using LLM agents with access to intelligent toolscited by 7
  7. 2025SIMSHIFT: A Benchmark for Adapting Neural Surrogates to Distribution Shiftscited by 6
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  9. 2025EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scalecited by 6
  10. 2025When is a System Discoverable from Data? Discovery Requires Chaoscited by 6
  11. 2025Towards a Foundation Model for Partial Differential Equations Across Physics Domainscited by 6
  12. 2025Towards a Physics Foundation Modelcited by 5
  13. 2026Structure-Preserving Learning Improves Geometry Generalization in Neural PDEscited by 5
  14. 2025FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulationcited by 4
  15. 2025T-SHRED: Symbolic Regression for Regularization and Model Discovery with Transformer Shallow Recurrent Decoderscited by 4
  16. 2025Physics-Grounded Motion Forecasting via Equation Discovery for Trajectory-Guided Image-to-Video Generationcited by 4
  17. 2025TC-LoRA: Temporally Modulated Conditional LoRA for Adaptive Diffusion Controlcited by 4
  18. 2026DiffusionRollout: Uncertainty-Aware Rollout Planning in Long-Horizon PDE Solvingcited by 4
  19. 2026CTF4Nuclear: Common Task Framework for Nuclear Fission and Fusion Modelscited by 4
  20. 2025Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoderscited by 3
  21. 2025AI for Scientific Discovery is a Social Problemcited by 3
  22. 2025AutoHood3D: A Multi-Modal Benchmark for Automotive Hood Design and Fluid-Structure Interactioncited by 3
  23. 2025Physics Steering: Causal Control of Cross-Domain Concepts in a Physics Foundation Modelcited by 3
  24. 2025AI Benchmark Democratization and Carpentrycited by 3
  25. 2026LEVDA: Latent Ensemble Variational Data Assimilation via Differentiable Dynamicscited by 3
  26. 2026MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systemscited by 3
  27. 2026Discovering Physical Directions in Weight Space: Composing Neural PDE Expertscited by 3
  28. 2026Emergent Transfer of a Physics Foundation Model from Simulation to Laboratory Turbulencecited by 3
  29. 2025Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solverscited by 2
  30. 2025Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow predictioncited by 2
  31. 2025An MLCommons Scientific Benchmarks Ontologycited by 2
  32. 2025MIMIC-MJX: Neuromechanical Emulation of Animal Behaviorcited by 2
  33. 2025Efficient Generative Transformer Operators For Million-Point PDEscited by 2
  34. 2025SynthPix: A lightspeed PIV image generatorcited by 2
  35. 2026Streaming Operator Inference for Model Reduction of Large-Scale Dynamical Systemscited by 2
  36. 2026Latent Generative Solvers for Generalizable Long-Term Physics Simulationcited by 2
  37. 2026Semigroup Consistency as a Diagnostic for Learned Physics Simulatorscited by 2
  38. 2025Data-Driven Forecasting of High-Dimensional Transient and Stationary Processes via Space-Time Projectioncited by 1

50 most cited of 134 All 134 (JSON)