Research map / Probabilistic and scientific modeling / Differential equations and PDEs
PDEBench: An Extensive Benchmark for Scientific Machine Learning
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| train U-Net with pushforward trick instead of one-step or fully autoregressive training (ablation) | U-Net · PDEBench PDEs | RMSE over unrolled steps | Helped |
| use FNO instead of U-Net | baseline surrogate · PDEBench forward problem | RMSE | Helped |
| use FNO instead of U-Net on inverse initial-condition problem | baseline surrogate · 1D PDEs | MSE of prediction | Helped |
| use FNO instead of U-Net | baseline surrogate · Darcy flow, small force term | normalized RMSE | Hurt |
| decrease diffusion coefficient (stronger discontinuity) | FNO · Burgers' | high-frequency fRMSE | Hurt |
| extrapolate in time beyond training steps | FNO · 1D Advection and Burgers' | RMSE | Hurt |
| use higher-resolution training samples (3D inviscid lower resolution vs 2D) | FNO · compressible Navier-Stokes | RMSE | Mixed |
| replace numerical solver with trained FNO at inference | FNO · diffusion-sorption | runtime (s): 59.83 -> 0.32 | Helped |
Closest papers by meaning
- SPDEBench: An Extensive Benchmark for Learning Stochastic PDEs (NeurIPS 2026 · similarity 0.92)
- PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs (NeurIPS 2024 · similarity 0.88)
- APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs (NeurIPS 2024 · similarity 0.88)
- Text2PDE: Latent Diffusion Models for Accessible Physics Simulation (ICLR 2025 · similarity 0.88)
- P$^2$C$^2$Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics (NeurIPS 2024 · similarity 0.88)
- CALM-PDE: Continuous and Adaptive Convolutions for Latent Space Modeling of Time-dependent PDEs (NeurIPS 2025 · similarity 0.87)
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