Allen-Cahn
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Solving PDE | Allen-Cahn | Relative Error0.0001 | 21 | |
| Forward PDE Solving | Allen–Cahn 10K-epoch | Relative L2 Error1.19 | 16 | |
| Learning PDE Solution Operators | Allen-Cahn 1D | Mean L2 Relative Error0.05 | 12 | |
| Solving Time-Dependent PDEs | Allen-Cahn | Relative L2 Error0 | 12 | |
| Learning PDE solution operators | 1D Allen-Cahn | Training Time (s)1.09 | 7 | |
| Inverse PDE Problem Solving | Allen-Cahn-2D | Success Rate100 | 6 | |
| 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) | MSE0 | 6 | |
| Solving Allen-Cahn Equation | Allen–Cahn (train) | Residual MSE1.54 | 5 | |
| PDE control | Allen-Cahn 20D | Evaluation Time119.8 | 5 | |
| PDE control | Allen-Cahn 10D | Evaluation Cost66.29 | 5 | |
| PDE dynamics prediction | Allen-Cahn 1D (test) | Relative Prediction Error (5-step)0.0055 | 4 | |
| PDE dynamics prediction | Allen-Cahn 2D (test) | 5-Step Relative Prediction Error0.37 | 3 | |
| PDE Inverse Problem | Allen-Cahn-2D (full) | SR100 | 3 | |
| 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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