Burgers
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Solving PDE | Burgers | Relative Error8 | 14 | |
| Solving Burgers equation | Burgers 1D | RMSE0.0036 | 12 | |
| Regression | Burgers Synthetic (test) | NRMSE0.0018 | 8 | |
| 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 | |
| Conservation-law discovery | burgers (test) | F167 | 4 | |
| Solving Time-Dependent PDEs | Burgers | Relative L2 Error0 | 4 | |
| Operator learning | Burgers (test) | Relative L2 Error (Test)0.012 | 3 | |
| Data Assimilation | Burgers R3 (test) | Average wall-time (s)0.023 | 3 | |
| PDE Solving | Burgers | Execution Time (s)2,150 | 3 | |
| Operator Learning | Burgers' Grid size 256 | Error0.0016 | 2 | |
| Learning PDE Dynamics | Burgers | Relative L2 Error0.0059 | 2 | |
| Timestepping | Burgers | NMSE0.108 | 2 | |
| Equation parameter regression | Burgers | Relative Error0.97 | 2 | |
| Solving nonlinear PDE | Burgers (test) | RMSE (T)0.0349 | 1 | |
| Inverse PDE Modeling | Burgers | Metric- | 0 |
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