Solving partial differential equations on Allen-Cahn equation Example 7 epsilon = 10−4
0.96L2 ErrorConventional PINN
Evaluation Results
| Method | Links | |
|---|---|---|
| Conventional PINNNumber of hidden layers=6, Neurons per layer=100, Number of collocation points=2 × 10^4, Number of boundary points=2 × 10^3, Number of initial points=10^32024.09 | 0.96 | |
| SA-PINNNumber of hidden layers=6, Neurons per layer=100, Number of collocation points=2 × 10^4, Number of boundary points=2 × 10^3, Number of initial points=10^3, Computational speed=~60 ms/iteration2024.09 | 2.1 | |
| W-PINNTranslation parameter γ=0.4, Resolutions (Jx, Jt)=[-5,6], [-5,5], Number of hidden layers=6, Neurons per layer=100, Number of collocation points=2 × 10^4, Number of boundary points=2 × 10^3, Number of initial points=10^3, Computational speed=30 ms/iteration2024.09 | 4.8 | |
| Time-adaptive approachNumber of hidden layers=6, Neurons per layer=100, Number of collocation points=2 × 10^4, Number of boundary points=2 × 10^3, Number of initial points=10^32024.09 | 8 |