Wave Equation
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Approximating Partial Differential Equations | Wave equation 39 | L_inf Error0 | 40 | |
| Forward PDE solving | Wave Equation | Rel. L2 Error1.09 | 12 | |
| PDE Discovery | 2D Wave equation | TPR100 | 10 | |
| Conservation Error Estimation | 3D Wave equation | Momentum Error3.84 | 8 | |
| Conservation Error Estimation | 1D Wave equation | Momentum Error1.34 | 8 | |
| Operator Learning | Wave Equation RPB (Out) | Relative Median L1 Error1.17 | 7 | |
| Operator Learning | Wave Equation RPB (In) | Relative Median L1 Test Error0.63 | 7 | |
| Solving Partial Differential Equations | Wave Equation vanilla PINN (test) | rRMSE0.94 | 3 | |
| PDE solution prediction and conservation | Wave Equation | Error u0.0195 | 3 | |
| PDE-Constrained Learning | Wave Equation Step IC | MSE (IBC)7.2 | 2 | |
| PDE-Constrained Learning | Wave Equation Sine Mix IC | MSE (IBC)4.6 | 2 | |
| PDE-Constrained Learning | Wave Equation Sine IC | MSE (IBC)1.1 | 2 | |
| PDE-Constrained Learning | Wave Equation Gauss Mix IC | MSE (IBC)2.7 | 2 | |
| PDE-Constrained Learning | Wave Equation Gauss IC | MSE (IBC)1.5 | 2 | |
| Verification of generalization error | 1D wave equation | Epsilon | del_Omega (Certified)0 | 1 |
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