1D Burgers' Equation
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| 1D Physics Modeling | 1D Burgers’ Equation (test) | MSE0.0054 | 38 | |
| Forward PDE Solving | 1D Burgers' equation standard synthetic (test) | Relative L2 Error0.0026 | 14 | |
| PDE Control | 1D Burgers' equation | Objective Function (J)0.0001 | 8 | |
| 1D Burgers' Equation Control | 1D Burgers' Equation PO-PC v1 (test) | J_actual0.0049 | 8 | |
| 1D Burgers' Equation Control | 1D Burgers' Equation FO-PC v1 (test) | J_actual0.0004 | 8 | |
| 1D Burgers' Equation Control | 1D Burgers' Equation PO-FC v1 (test) | J_actual0.011 | 7 | |
| Physics-informed adaptation | 1D Burgers Equation BC adapt | Full PDE MSE1.84 | 5 | |
| Physics-informed adaptation | 1D Burgers Equation IC adapt | Full PDE MSE1.53 | 5 | |
| Parameter Estimation | 1D Burgers' Equation Inverse Problem Setting | Estimated Kappa 11.9821 | 5 | |
| Inverse PDE Solving | 1D Burgers equation inverse problem | Relative L2 Error4.02 | 5 | |
| Forward Problem | 1D Burgers equation | Relative L2 Error1.06 | 5 | |
| Rollout Prediction | 1D Burgers' equation (400-step rollout) | RMSE0.13 | 5 | |
| Neural PDE Solving | 1D Burgers Equation | Residual Bound0.124 | 1 |
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