Poisson
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| PDE Solving | Poisson | Time (s)19.95 | 55 | |
| PDE Solving | Poisson | L2 Error0 | 30 | |
| Inverse problem | Poisson | PDE Residual0.44 | 21 | |
| Eigenvalue problem solving | Poisson Dimension 2500 Precision 1e-12 | Average Computation Time (s)12.85 | 18 | |
| Forward PDE solving | Poisson | Relative L2 Error0.038 | 15 | |
| Inverse PDE solving | Poisson | Relative Error0.123 | 13 | |
| PDE Forward Problem | Poisson Noisy | L2 Relative Error6.52 | 12 | |
| Forward PDE Solving | Poisson (test) | Relative H1 Error0.181 | 12 | |
| Temporal Point Process modeling | Poisson synthetic (test) | NLL0.9945 | 11 | |
| PDE Reconstruction | Poisson 3% uniformly random measurements | Coefficient Rel L2 Error (%)7.81 | 10 | |
| Inverse PDE solving | Poisson Full Observation | L2 Relative Error10.2 | 9 | |
| Forward PDE solving | Poisson Full Observation | L2 Relative Error0.7 | 9 | |
| Forward problem | Poisson | PDE Residual0.87 | 9 | |
| Conformal Prediction | Poisson | CCC (%)98.8 | 8 | |
| Uncertainty-bound prediction | Poisson | MC (%)92.34 | 8 | |
| Neural Operator Learning | POISSON C-SINES | Median Relative L1 Error1 | 8 | |
| PDE solving | Poisson 2D (test) | L2 Rel. Error0.0029 | 8 | |
| PDE Solving | Poisson (train) | Error0 | 7 | |
| PDE Solving | Poisson (val) | Error0 | 7 | |
| PDE Inverse Problem | Poisson Noisy | L2 Relative Error41.14 | 7 | |
| Image Reconstruction | Poisson | MSE0.0002 | 6 | |
| Conditional source inference | Poisson 256 samples (test) | Relative L2 Error0.399 | 6 | |
| PDE Solving | Poisson Neumann BC | Test Error0.0002 | 5 | |
| Inverse | Poisson 30% noise corruption 1.0 (test) | L2 Relative Error32.16 | 5 | |
| Forward | Poisson 30% noise corruption 1.0 (test) | L2 Relative Error0.1122 | 5 |
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