Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Group Equivariant Fourier Neural Operators for Partial Differential Equations
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| encode p4 equivariance in Fourier layers | FNO · NS | R-MSE (%): 8.41(0.41) -> 4.78(0.39) | Helped |
| encode p4 equivariance in Fourier layers | FNO · NS-sym | R-MSE (%): 4.21(0.12) -> 2.24(0.09) | Helped |
| encode p4 equivariance in Fourier layers | FNO · SWE | R-MSE (%): 18.45(0.89) -> 14.96(0.06) | Helped |
| encode p4m equivariance instead of p4 | G-FNO · SWE-sym | R-MSE (×10^-3): 1.21(0.02) -> 1.11(0.17) | Mixed |
| add equivariant layers progressively (ablation) | FNO on NS · NS | R-MSE (%): 8.41(0.41) -> 7.17(0.51) -> 6.30(0.82) -> 6.12(0.44) -> 4.78(0.39) | Helped |
| train with Markov rather than Teacher Forcing (ablation) | G-FNO-p4 · NS super-resolution | R-MSE (%): 43.41(0.12) -> 43.35(0.24) | Mixed |
| train recurrently rather than Teacher Forcing (ablation) | G-FNO-p4 · NS super-resolution | R-MSE (%): 43.41(0.12) -> 42.36(0.23) | Helped |
| remove positional encoding (ablation) | G-FNO-p4 · NS | R-MSE (%): 4.78(0.39) -> 4.47(0.21) | Helped |
| use Cartesian instead of symmetric positional encoding (ablation) | G-FNO-p4 · NS | R-MSE (%): 4.78(0.39) -> 4.39(0.25) | Helped |
| replace original kernel parameterization with steerable parameterization (ablation) | G-FNO-p4 · NS | R-MSE (%): 4.78(0.39) -> 20.87(1.25) | Hurt |
| use radial kernels | Fourier operator on SWE-sym · SWE-sym, 2D | R-MSE (×10^-3): 1.21(0.02) -> 0.71(0.03) | Helped |
| use radial kernel inductive bias | Fourier operator across other reported settings · Navier-Stokes and remaining SWE settings | R-MSE | Hurt |
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