2D Heat Equation
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Inverse mapping | 2D Heat Equation 16 x 16 finite element mesh (test) | Average Relative Error44.99 | 16 | |
| Forward mapping | 2D Heat Equation 16 x 16 finite element mesh (test) | Average Relative Error1.09 | 14 | |
| 2D heat conductivity inversion | 2D heat equation S=1500 | Best Relative Error32.1 | 9 | |
| 2D heat conductivity inversion | 2D heat equation S=1000 | Best Relative Error0.327 | 9 | |
| Inverse Problem Solving | 2D heat equation inverse problem | Relative L2 Error1.59 | 5 | |
| Inverse Parameter Estimation | 2D Heat Equation | Kappa Hat Estimate0.984 | 5 | |
| Forward PDE Solving | 2D Heat Equation homogeneous Dirichlet condition u = 0 (test) | Rel. L2 Error3.09 | 5 | |
| PDE Constrained Optimization | 2D Heat Equation | Metric- | 0 |
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