Research map / Probabilistic and scientific modeling / Differential equations and PDEs
DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply DPM gradient manipulation to PINN-R | PINN-R · Viscous Burgers extrapolation | relative L2-norm error: 0.333 -> 0.092 | Helped |
| Apply DPM gradient manipulation to PINN-R | PINN-R · Inviscid Burgers extrapolation | relative L2-norm error: 0.095 -> 0.090 | Helped |
| Apply DPM gradient manipulation to PINN-R | PINN-R · Allen-Cahn extrapolation | relative L2-norm error: 0.286 -> 0.182 | Helped |
| Apply DPM gradient manipulation to PINN-R | PINN-R · Schrödinger extrapolation | relative L2-norm error: 0.212 -> 0.141 | Helped |
| Add dynamic control of δ to DPM (ablation) | PINN-D1 · Viscous Burgers extrapolation | relative L2-norm error: 0.106 -> 0.092 | Helped |
| Add dynamic control of δ to DPM (ablation) | PINN-D1 · Inviscid Burgers extrapolation | relative L2-norm error: 0.083 -> 0.090 | Hurt |
| Add dynamic control of δ to DPM (ablation) | PINN-D1 · Allen-Cahn extrapolation | relative L2-norm error: 0.246 -> 0.182 | Helped |
| Add dynamic control of δ to DPM (ablation) | PINN-D1 · Schrödinger extrapolation | relative L2-norm error: 0.314 -> 0.141 | Helped |
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