# RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data

arXiv: https://arxiv.org/abs/2601.01829 · HTML: https://mlsanity.com/paper/2601.01829/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 98 references that are in the map.
- First posted on arXiv 5 Jan 2026.

## Builds on (most cited first, 30 of 39)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [Simulation Intelligence: Towards a New Generation of Scientific Methods](https://mlsanity.com/paper/2112.03235/) (2021)
- [InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences](https://mlsanity.com/paper/2503.11043/) (2025)
- [Scientific Machine Learning Benchmarks](https://mlsanity.com/paper/2110.12773/) (2021)
- [APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs](https://mlsanity.com/paper/2411.00180/) (2024)
- [CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics](https://mlsanity.com/paper/2310.05963/) (2023)
- [ChaosBench: A Multi-Channel, Physics-Based Benchmark for Subseasonal-to-Seasonal Climate Prediction](https://mlsanity.com/paper/2402.00712/) (2024)
- [Wavelet Diffusion Neural Operator](https://mlsanity.com/paper/2412.04833/) (2024)
- [Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey](https://mlsanity.com/paper/2408.12171/) (2024)
- [LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suite](https://mlsanity.com/paper/2309.16342/) (2023)
- [Compositional Generative Inverse Design](https://mlsanity.com/paper/2401.13171/) (2024)

## Built on by (most cited first, 16 of 16)

- [PDEAgent-Bench: A Multi-Metric, Multi-Library Benchmark for PDE Solver Generation](https://mlsanity.com/paper/2605.09636/) (2026)
- [Emergent Transfer of a Physics Foundation Model from Simulation to Laboratory Turbulence](https://mlsanity.com/paper/2606.01470/) (2026)
- [Data-driven discovery of governing differential equations across physical systems](https://mlsanity.com/paper/2606.09638/) (2026)
- [A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modeling](https://mlsanity.com/paper/2606.24696/) (2026)
- [Sim+Real: Joint Simulation-Experiment Training Improves Balanced Prediction in Physical Systems](https://mlsanity.com/paper/2610.01974/) (2026)
- [CarCrashNet: A Large-Scale Dataset and Hierarchical Neural Solver for Data-Driven Structural Crash Simulation](https://mlsanity.com/paper/2605.07098/) (2026)
- [PhysGuard: Fisher-Guided Gradient Projection for Sim-to-Real Neural PDE Surrogates](https://mlsanity.com/paper/2606.16602/) (2026)
- [ThousandWorlds: A benchmark for climate emulation of potentially habitable exoplanets](https://mlsanity.com/paper/2606.18338/) (2026)
- [Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows](https://mlsanity.com/paper/2607.22280/) (2026)
- [PhysFieldBench: Can Multimodal Models Understand Physical Fields?](https://mlsanity.com/paper/2609.34072/) (2026)
- [Transolver-σ: Joint Spectral-Physical Subspace Modeling for Neural PDE Solving](https://mlsanity.com/paper/2609.37279/) (2026)
- [Beyond Simulation: Retain-and-Repair Neural Operators for Real-World Adaptation](https://mlsanity.com/paper/2609.39387/) (2026)
- [Do Better Scores Mean Better Physics? Physics-Grounded Explanations for Sim2Real Neural Operators](https://mlsanity.com/paper/2610.00415/) (2026)
- [Seq-Flow: Efficient Probabilistic Forecasting with Self-Rollout Error Control](https://mlsanity.com/paper/2610.10440/) (2026)
- [Interactive 4D Volumetric Liquid Forecasting under Moving-Solid Interaction](https://mlsanity.com/paper/2610.16167/) (2026)
- [ReAl: Refine neural operators via aligning dynamical flow](https://mlsanity.com/paper/2610.20369/) (2026)

## Abstract (arXiv)

Predicting the evolution of complex physical systems remains a central problem in science and engineering. Despite rapid progress in scientific Machine Learning (ML) models, a critical bottleneck is the lack of expensive real-world data, resulting in most current models being trained and validated on simulated data. Beyond limiting the development and evaluation of scientific ML, this gap also hinders research into essential tasks such as sim-to-real transfer. We introduce RealPDEBench, the first benchmark for scientific ML that integrates real-world measurements with paired numerical simulations. RealPDEBench consists of five datasets, three tasks, eight metrics, and ten baselines. We first present five real-world measured datasets with paired simulated datasets across different complex physical systems. We further define three tasks, which allow comparisons between real-world and simulated data, and facilitate the development of methods to bridge the two. Moreover, we design eight evaluation metrics, spanning data-oriented and physics-oriented metrics, and finally benchmark ten representative baselines, including state-of-the-art models, pretrained PDE foundation models, and a traditional method. Experiments reveal significant discrepancies between simulated and real-world data, while showing that pretraining with simulated data consistently improves both accuracy and convergence. In this work, we hope to provide insights from real-world data, advancing scientific ML toward bridging the sim-to-real gap and real-world deployment. Our benchmark, datasets, and instructions are available at https://realpdebench.github.io/.