Burgers' Equation
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Model Reduction | Burgers' Equation Shift Trajectory Manifold | Relative Test Error1.16 | 140 | |
| PDE Solving | 1d Burgers' equation (test) | Relative Error0.0079 | 85 | |
| PDE Modeling | Burgers' Equation various resolutions (val) | Relative L2 Error0.0018 | 36 | |
| Parameter Identification | Burgers' equation Case 3.3 | MSE0 | 32 | |
| Operator Learning Rollout Prediction | Burgers' Equation E1 | MSE0 | 28 | |
| Solving Partial Differential Equations | Burgers' equation viscosity ν = 0.02 | Relative L2 Error0.0001 | 20 | |
| PDE solving | Burgers' equation | L2 Relative Error0.0001 | 18 | |
| Solving PDEs | Burgers' Equation (test) | Max Relative L2 Error0.0016 | 11 | |
| Stochastic Filtering | Burgers' equation (test) | RMSE0.0751 | 10 | |
| Filtering | Burgers' equation nu=0.01 | RMSE0.114 | 10 | |
| Equation Reconstruction | Burgers equation (test) | L2 Error4.19 | 9 | |
| PDE discovery | Burgers' equation multiple-source dataset 1000 data per case | Discovered PDE Structure1 | 8 | |
| PDE discovery | Burgers' equation multiple-source 100 data per case | PDE Structure Match1 | 8 | |
| Solving Nonlinear PDEs | Burgers’ equation n = 32 (test) | Relative L2 Error0.0004 | 8 | |
| Equation Discovery | Burgers' Equation PDE (Noise Levels: 0%, 1%, 10% (large)) | RMSE (0% Noise)0.754 | 8 | |
| Solving Partial Differential Equations | Burgers Equation | Wall-clock Time (CPU)2.18 | 6 | |
| Operator Learning | one-dimensional Burgers' equation | Relative L2 Error (EL2)0.0486 | 6 | |
| PDE Discovery | Burgers’ equation (0.2% Noise) | MSE0 | 5 | |
| Neural PDE Solving | Burgers equation periodic boundary conditions spectral-1024 reference (T=4) | Relative L2 Error0.0002 | 5 | |
| Neural PDE Solving | Burgers equation periodic boundary conditions spectral-1024 reference (T=3) | Relative L2 Error0.0001 | 5 | |
| Neural PDE Solving | Burgers equation periodic boundary conditions spectral-1024 reference (T=2) | Relative L2 Error0 | 5 | |
| Neural PDE Solving | Burgers equation periodic boundary conditions spectral-1024 reference (T=1) | Relative L2 Error0 | 5 | |
| Trajectory Reconstruction | Burgers' Equation (Boundary Condition) | Reconstruction Error (RE)0.32 | 5 | |
| Learning Spatiotemporal Dynamics | Burgers Equation (test) | RMSE0.0064 | 5 | |
| Inverse-problem estimation | Burgers equation 5% noise | Relative Viscosity Error1.78 | 4 |
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