Allen-Cahn
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Solving PDE | Allen-Cahn | Relative Error0.03 | 14 | |
| Learning PDE Solution Operators | Allen-Cahn 1D | Mean L2 Relative Error0.05 | 12 | |
| Learning PDE solution operators | 1D Allen-Cahn | Training Time (s)1.09 | 7 | |
| PDE solving | Allen-Cahn | Inference Time (s)1.33 | 6 | |
| Spatiotemporal PDE Solving | Allen-Cahn | MSE0.0088 | 6 | |
| PDE Solving | Allen-Cahn (test) | Relative L1 Error (Final Time)1.03 | 6 | |
| Solving nonlinear PDE | Allen-Cahn (test) | Relative L2 Error0 | 5 | |
| Solving Time-Dependent PDEs | Allen-Cahn | Relative L2 Error0 | 4 | |
| Solving high-dimensional inseparable PDEs | Allen-Cahn 100KD | Error0.0543 | 3 | |
| Solving high-dimensional inseparable PDEs | Allen-Cahn 10KD | Error0.0001 | 3 | |
| Solving high-dimensional inseparable PDEs | Allen-Cahn 1KD | Error0.0526 | 3 | |
| Solving high-dimensional inseparable PDEs | Allen-Cahn 100D | Error3.97 | 3 | |
| Operator Learning | Allen-Cahn phase-field | Mean Relative L2 Error5.85 | 2 | |
| Operator Learning | Allen-Cahn phase-field (test) | Metric- | 0 |
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