Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add sequential transfer-learning updates to DeepONet during time marching | DeepONet · Reaction diffusion, T=50 | relative L2 error: 1.69e0 -> 1.52e-3 | Helped |
| Add sequential transfer-learning updates to DeepONet during time marching | DeepONet · 1D Allen-Cahn, T=50 | time-average relative prediction error: 1.13e0 -> 9.25e-4; 1.33e0 -> 9.64e-4; 1.29e0 -> 2.16e-2 | Helped |
| Add sequential transfer-learning updates to DeepONet during time marching | DeepONet · 1D Cahn-Hilliard, T=50 | time-average relative prediction error: 9.43e-1 -> 1.04e-2 | Helped |
| Add sequential transfer-learning updates to DeepONet during time marching | DeepONet · 2D Navier-Stokes, T=10 | relative prediction error: 9.95e-1 -> 1.41e-2; 1.02e0 -> 1.07e-2; 9.96e-1 -> 3.35e-2; 1.04e0 -> 9.42e-2 | Helped |
| Add sequential transfer-learning updates to DeepONet during time marching | DeepONet · Radiative transfer, 1D and 2D, T=10 | relative prediction error: 3.06e-1 -> 1.52e-2; 3.74e-1 -> 5.52e-3; 3.58e-1 -> 2.19e-2; 2.37e0 -> 8.93e-3 | Helped |
| Use CONT DeepONet trained with an aggregated time-window loss instead of single-step DeepONet (ablation) | DeepONet · Reaction diffusion | relative L2 error: 7.95e-2 -> 5.38e-3; 4.17e-1 -> 1.95e-3 | Mixed |
| Use the second-order Crank-Nicolson time scheme with TL-DeepONet (ablation) | TL-DeepONet · Reaction diffusion, T=50 | relative error: 1.78e-3 -> 4.91e-4; 2.63e-3; 9.53e-3 | Mixed |
| Increase the Crank-Nicolson time step from 0.05 to 0.4 (ablation) | TL-DeepONet 2nd · Reaction diffusion, T=50 | relative error: 1.78e-3 -> 9.53e-3 | Hurt |
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