mlsanityData to 7 Oct 2026

PDEBENCH: An Extensive Benchmark for Scientific Machine Learning

arXiv 2210.07182 ↗First posted 13 Oct 2022cs.LG cs.CV physics.flu-dyncited by 396

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Cited by 29 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Machine learning-based modeling of physical systems has experienced increased interest in recent years. Despite some impressive progress, there is still a lack of benchmarks for Scientific ML that are easy to use but still challenging and representative of a wide range of problems. We introduce PDEBench, a benchmark suite of time-dependent simulation tasks based on Partial Differential Equations (PDEs). PDEBench comprises both code and data to benchmark the performance of novel machine learning models against both classical numerical simulations and machine learning baselines. Our proposed set of benchmark problems contribute the following unique features: (1) A much wider range of PDEs compared to existing benchmarks, ranging from relatively common examples to more realistic and difficult problems; (2) much larger ready-to-use datasets compared to prior work, comprising multiple simulation runs across a larger number of initial and boundary conditions and PDE parameters; (3) more extensible source codes with user-friendly APIs for data generation and baseline results with popular machine learning models (FNO, U-Net, PINN, Gradient-Based Inverse Method). PDEBench allows researchers to extend the benchmark freely for their own purposes using a standardized API and to compare the performance of new models to existing baseline methods. We also propose new evaluation metrics with the aim to provide a more holistic understanding of learning methods in the context of Scientific ML. With those metrics we identify tasks which are challenging for recent ML methods and propose these tasks as future challenges for the community. The code is available at https://github.com/pdebench/PDEBench.

Key facts. Cited by 396 papers in the map (data through 7 Oct 2026). Builds on 27 of its 97 references that are in the map. First posted on arXiv 13 Oct 2022.

Builds on

27 of 97 references.

References · 27

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2018Neural Ordinary Differential Equationscited by 3,733
  5. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  6. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  7. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  8. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  9. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  10. 2021Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulationcited by 375
  11. 2022Message Passing Neural PDE Solverscited by 368
  12. 2019Towards Physics-informed Deep Learning for Turbulent Flow Predictioncited by 203
15 more
  1. 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
  2. 2017PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparisoncited by 139
  3. 2021Learned Coarse Models for Efficient Turbulence Simulationcited by 90
  4. 2021Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equationscited by 68
  5. 2021Simulation Intelligence: Towards a New Generation of Scientific Methodscited by 68
  6. 2020NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation frameworkcited by 58
  7. 2021HyperPINN: Learning parameterized differential equations with physics-informed hypernetworkscited by 38
  8. 2022Physical Design using Differentiable Learned Simulatorscited by 37
  9. 2022JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flowscited by 36
  10. 2021An Extensible Benchmark Suite for Learning to Simulate Physical Systemscited by 24
  11. 2021Composing Partial Differential Equations with Physics-Aware Neural Networkscited by 21
  12. 2020Variational Autoencoding of PDE Inverse Problemscited by 9
  13. 2021A Large-Scale Benchmark for the Incompressible Navier-Stokes Equationscited by 4
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 59; 2024: 82; 2025: 108; 2026: 144.

396 papers.

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  1. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  2. 2023Neural Operators for Accelerating Scientific Simulations and Designcited by 218
  3. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 205
  4. 2024Poseidon: Efficient Foundation Models for PDEscited by 186
  5. 2024DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Trainingcited by 137
  6. 2024The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learningcited by 134
  7. 2024BetterBench: Assessing AI Benchmarks, Uncovering Issues, and Establishing Best Practicescited by 112
  8. 2023Multiple Physics Pretraining for Physical Surrogate Modelscited by 90
  9. 2023PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEscited by 84
  10. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulationcited by 65
  11. 2024Neural Operators with Localized Integral and Differential Kernelscited by 59
  12. 2024Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEscited by 58
38 more
  1. 2023CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problemscited by 54
  2. 2024CViT: Continuous Vision Transformer for Operator Learningcited by 47
  3. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 46
  4. 2024Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolationcited by 45
  5. 2023Training neural operators to preserve invariant measures of chaotic attractorscited by 43
  6. 2023Group Equivariant Fourier Neural Operators for Partial Differential Equationscited by 42
  7. 2023CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamicscited by 40
  8. 2024ChaosBench: A Multi-Channel, Physics-Based Benchmark for Subseasonal-to-Seasonal Climate Predictioncited by 40
  9. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generationcited by 37
  10. 2023Learning Neural PDE Solvers with Parameter-Guided Channel Attentioncited by 37
  11. 2025CodePDE: An Inference Framework for LLM-driven PDE Solver Generationcited by 37
  12. 2023Cross-Modal Fine-Tuning: Align then Refinecited by 34
  13. 2024TimeDiT: General-purpose Diffusion Transformers for Time Series Foundation Modelcited by 33
  14. 2024PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamicscited by 33
  15. 2024Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learningcited by 32
  16. 2024PINNACLE: PINN Adaptive ColLocation and Experimental points selectioncited by 31
  17. 2024Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solverscited by 31
  18. 2024On the Benefits of Memory for Modeling Time-Dependent PDEscited by 30
  19. 2023Koopman neural operator as a mesh-free solver of non-linear partial differential equationscited by 29
  20. 2023Self-Supervised Learning with Lie Symmetries for Partial Differential Equationscited by 29
  21. 2024Wavelet Diffusion Neural Operatorcited by 28
  22. 2023A Unified Framework for U-Net Design and Analysiscited by 27
  23. 2024UPS: Efficiently Building Foundation Models for PDE Solving via Cross-Modal Adaptationcited by 27
  24. 2024Recent Advances on Machine Learning for Computational Fluid Dynamics: A Surveycited by 27
  25. 2023LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suitecited by 26
  26. 2025Walrus: A Cross-Domain Foundation Model for Continuum Dynamicscited by 26
  27. 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
  28. 2022Incremental Spatial and Spectral Learning of Neural Operators for Solving Large-Scale PDEscited by 25
  29. 2023HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetworkcited by 25
  30. 2024Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operatorscited by 25
  31. 2024Zero-shot forecasting of chaotic systemscited by 25
  32. 2024HAMLET: Graph Transformer Neural Operator for Partial Differential Equationscited by 24
  33. 2024Scaling physics-informed hard constraints with mixture-of-expertscited by 24
  34. 2024Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspectivecited by 24
  35. 2023A Neural PDE Solver with Temporal Stencil Modelingcited by 22
  36. 2023Harnessing the Power of Neural Operators with Automatically Encoded Conservation Lawscited by 22
  37. 2024Active Learning for Neural PDE Solverscited by 22
  38. 2024VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Predictioncited by 22

50 most cited of 396 All 396 (JSON)