Research map / Probabilistic and scientific modeling / Differential equations and PDEs
PDE-Net: Learning PDEs from Data
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use learnable, moment-constrained filters instead of frozen filters (ablation) | PDE-Net · Linear convection-diffusion equation | normalized prediction error | Helped |
| Use learnable, moment-constrained filters instead of frozen filters (ablation) | PDE-Net · Diffusion equation with nonlinear source | normalized prediction error | Helped |
| Stack multiple shared-parameter δt-blocks rather than using a single block (ablation) | PDE-Net · Linear convection-diffusion equation | long-term prediction stability | Helped |
| Increase filter size from 5×5 to 7×7 (ablation) | PDE-Net · Linear convection-diffusion equation | length of reliable predictions: about 10 times | Helped |
| Increase filter size from 5×5 to 7×7 (ablation) | PDE-Net · Linear convection-diffusion equation | coefficient estimation error | No clear effect |
| Remove moment constraints and filter-based initialization and warm-up (ablation) | PDE-Net (Freed-PDE-Net) · Linear convection-diffusion equation | normalized prediction error | Helped |
| Remove moment constraints and filter-based initialization and warm-up (ablation) | PDE-Net (Freed-PDE-Net) · Linear convection-diffusion equation | PDE identifiability | Hurt |
| Use prior knowledge that the PDE order is at most 2 rather than at most 4 (ablation) | PDE-Net · Linear convection-diffusion equation | prediction error | Hurt |
| Use prior knowledge that the PDE order is at most 2 rather than at most 4 (ablation) | PDE-Net · Linear convection-diffusion equation | variance of prediction errors | Helped |
| Use more δt-blocks (ablation) | PDE-Net · Linear convection-diffusion equation | coefficient estimation error | Helped |
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