Heat equation
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Fixed-time learning | Heat Equation 24 (test) | Empirical L2 Error0.019 | 84 | |
| Spatio-temporal learning | Heat equation (24) m=30 (test) | Empirical L2-error0.031 | 14 | |
| Spatio-temporal learning | Heat equation 24 m=20 (test) | Empirical L2 Error0.081 | 14 | |
| Spatio-temporal learning | Heat equation (24) m=10 (test) | L2 Error (Empirical)0.029 | 14 | |
| PDE Solving | 5D-Heat equation | Relative L2 Error0.0008 | 10 | |
| Solving Constrained PDEs | Heat Equation | MMSE0.845 | 7 | |
| Solving Heat Equation | heat equation multi-frequency initial condition | Best Relative L2 Error1.41 | 5 | |
| Heat Equation | Heat Equation 20K epochs | L1 Error0.0018 | 5 | |
| Equation Discovery | Heat Equation PDE Noise Levels: 0%, 0.1%, 15% (large) | Mp1 | 4 | |
| PDE Solving | Heat Equation | L2 Error0.0015 | 3 | |
| PDE-Constrained Learning | Heat Equation Step IC | MSE (IBC)1.8 | 2 | |
| PDE-Constrained Learning | Heat Equation Sine Mix IC | MSE (IBC)2 | 2 | |
| PDE-Constrained Learning | Heat Equation Sine IC | MSE (IBC)2.4 | 2 | |
| PDE-Constrained Learning | Heat Equation Gauss IC | MSE (IBC)2.4 | 2 | |
| PDE-Constrained Learning | Heat Equation Poly IC | MSE (IBC)8.2 | 2 |
Showing 15 of 15 rows