Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Learning Neural PDE Solvers with Convergence Guarantees
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use learned Conv3 update corrections instead of Jacobi | Poisson solver · Square | computation cost (layers / Jacobi): 0.219 | Helped |
| Use learned Conv3 update corrections instead of Jacobi | Poisson solver · L-shape | computation cost (multiply-add ops / Jacobi): 0.423 | Helped |
| Use learned Conv3 update corrections instead of Jacobi | Poisson solver · Cylinders | computation cost (multiply-add ops / Jacobi): 0.426 | Helped |
| Use learned U-Net2 updates instead of Multigrid2 | Poisson solver · Square | computation cost (multiply-add ops / Multigrid2): 0.205 | Helped |
| Use learned U-Net2 updates instead of Multigrid2 | Poisson solver · L-shape | computation cost (multiply-add ops / Multigrid2): 0.203 | Helped |
| Use learned U-Net2 updates instead of Multigrid2 | Poisson solver · Cylinders | computation cost (multiply-add ops / Multigrid2): 0.204 | Helped |
| Use learned U-Net2 updates instead of Multigrid2 | Poisson solver · Square-Poisson | computation cost (multiply-add ops / Multigrid2): 0.178 | Helped |
| Increase Conv depth from 3 to 4 layers (ablation) | Learned Conv solver · Square | computation cost (layers / Jacobi): 0.219 -> 0.224 | Hurt |
| Increase U-Net subsampling depth from 2 to 3 (ablation) | Learned U-Net solver · Square | computation cost (layers / Multigrid baseline): 0.091 -> 0.220 | Hurt |
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