KdV equation
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| PDE Discovery | KdV equation | TPR100 | 10 | |
| Conservation Error Estimation | 3D KdV equation | Momentum Conservation Error1.25 | 8 | |
| Conservation Error Estimation | 1D KdV equation | Momentum Conservation Error1.4 | 8 | |
| Autoregressive PDE Solving (KdV 20s) | KdV equation LPSDA protocol (in-distribution) | NMSE0.0047 | 4 | |
| Numerical integration | KdV equation T=1.0, N=1024, γ=0.5 | L2 Error (τ=2^-4)0.0042 | 4 | |
| PDE solution prediction and conservation | KdV Equation | Error u0.0735 | 3 |
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