PDEBench
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| PDE Solving | PDEBench Diff.Sorp (test) | nRMSE0.0016 | 65 | |
| PDE Solving | PDEBench Diff.Reac 1D (test) | nRMSE0.0014 | 41 | |
| Operator Learning | PDEBench SWE | L2 Relative Error (L2RE)0.0007 | 28 | |
| Operator Learning | PDEBench DR | L2RE0.0064 | 28 | |
| PDE Solving | PDEBench rdb (test) | nRMSE11.3 | 28 | |
| Rollout Prediction | PDEBench rdb (test) | nRMSE0.071 | 28 | |
| Rollout Prediction | PDEBench diff-sorp (test) | nRMSE0.105 | 28 | |
| Operator Learning | PDEBench CNS (η=0.1, ζ=0.01) | L2 Relative Error0.0032 | 25 | |
| Operator Learning | PDEBench CNS (η=0.1, ζ=0.1) | L2 Relative Error (L2RE)0.0079 | 25 | |
| Operator Learning | PDEBench CNS (η=1, ζ=0.01) | L2RE0.491 | 25 | |
| Operator Learning | PDEBench CNS (η=1, ζ=0.1) | L2RE0.0043 | 25 | |
| Advection-Diffusion-Reaction | PDEBench ADR 64 x 64 (evaluation regime nc=2, Pe=1, Da=0.1) | Relative L2 Error0.028 | 20 | |
| PDE Forecasting | PDEBench RDB (test) | Regret Knee-0.9 | 16 | |
| Regret assessment | PDEBench RDB full-oracle case-level | Regret Knee-0.9 | 16 | |
| Context window selection for PDE forecasting | PDEBench DiffReact (full-oracle case-level) | Regret Knee-0.8 | 16 | |
| Neural PDE rollout | PDEBench Public metadata-hidden protocol (test) | nRMSE1.25 | 15 | |
| Burgers' Equation | PDEBench | Latency (s)0.72 | 14 | |
| 1D Diffusion-Sorption | PDEBench | Latency (s)1.97 | 14 | |
| 1D Diffusion-Reaction | PDEBench | Latency (s)0.99 | 14 | |
| PDE Solving | PDEBench 2D Shallow Water Equations | Relative L2 Error0.0014 | 11 | |
| Solving Diffusion Equation | PDEBench DIFF 2D (test) | Test Error0.0073 | 10 | |
| PDE Prediction | PDEBench 2D Shallow Water Equations (SWE) (test) | Prediction Error0.0017 | 10 | |
| PDE Solving | PDEBench 1D Burgers | Relative L2 Error0.63 | 9 | |
| PDE Solving | PDEBench 1D Advection | Relative L2 Error0.28 | 9 | |
| PDE Solving | PDEBench Advection (test) | nRMSE0.0032 | 9 |
Showing 25 of 91 rows