Burgers
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Solving PDE | Burgers | Relative Error0.26 | 24 | |
| Forward PDE problem solving | Burgers’ | Relative L2 Error0.0046 | 19 | |
| Forward PDE Solving | Burgers 10K-epoch | Relative L2 Error1.1 | 16 | |
| Neural Operator Learning | 2D Burgers | Relative L2 Error0.24 | 15 | |
| Solving Burgers equation | Burgers 1D | RMSE0.0036 | 15 | |
| Partial Differential Equation Solving | Burgers Case E8 Mixed BC | Relative L2 Error0.0376 | 12 | |
| Partial Differential Equation Solving | Burgers Case E6 2D | Relative L2 Error0.011 | 12 | |
| PDE solving | Burgers | Relative L2 Error0.0097 | 10 | |
| Spatial super-resolution | Burgers spatial super-resolution (test) | NRMSE2.488 | 9 | |
| PDE Solving | Burgers 2D | Relative L2 Error15.7 | 9 | |
| Reduced Order Modeling | Burgers problem (t ∈ [0.004, 0.5]) | Wall-clock Time (s)0.052 | 8 | |
| PDE Rollout Prediction | Burgers trajectory set (test) | Rollout Relative H14.18 | 8 | |
| PDE Rollout Simulation | Burgers (test) | Relative L2 Error4.16 | 8 | |
| Regression | Burgers Synthetic (test) | NRMSE0.0018 | 8 | |
| Long-horizon stability | Burgers 1D (test) | MSE0.045 | 7 | |
| Solving Partial Differential Equations | Burgers v = 1/100pi | Relative L2 Error1.38 | 7 | |
| PDE dynamics forecasting | Burgers OOD | nMSE0.0108 | 7 | |
| PDE dynamics forecasting | Burgers (ID) | nMSE0.0012 | 7 | |
| PDE Solving | Burgers' (test) | Relative Error4.27 | 7 | |
| Functional Mapping | Burgers Synthetic | MNLL-4.27 | 6 | |
| PDE Solving | Burgers (nu = 1/100pi) (test) | Relative L2 Error0 | 6 | |
| Dense field reconstruction | Burgers PhysBR (test) | Mean Rel L2 Error6 | 5 | |
| Solving Burgers' equation with PINNs | Burgers | Validation L2 Error0.011 | 4 | |
| Constrained PDE Generative Modeling | Burgers | MMSE0.0356 | 4 | |
| Constrained PDE Generative Modeling | Burgers BC | MMSE (Mean Squared Error)0.0018 | 4 |
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