Research map / Learning theory and algorithms / Sample complexity
Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace linear reconstruction (DeepONet) with nonlinear reconstruction (shift-DeepONet) | DeepONet on advection/Burgers · Linear Advection and Burgers' equation | relative median L1 error: about 2.9x lower on advection (7.95% to 2.76%); about 3.6x lower on Burgers (28.5% to 7.83%) | Helped |
| Replace linear reconstruction (DeepONet) with nonlinear reconstruction (FNO) | DeepONet on advection/Burgers · Linear Advection and Burgers' equation | relative median L1 error: advection 7.95% to 0.71%; Burgers 28.5% to 1.57% (about 20x) | Helped |
| Use FNO instead of shift-DeepONet | nonlinear reconstruction methods · Linear Advection, Burgers, Lax-Sod shock tube | relative median L1 error: advection 2.76% to 0.71%; Burgers 7.83% to 1.57%; Sod 2.76% to 1.56% | Helped |
| Replace linear reconstruction (DeepONet) with nonlinear reconstruction (shift-DeepONet and FNO) | DeepONet on 2D Riemann problem · 2D four-quadrant Riemann problem | relative median L1 error: DeepONet 0.89% vs shift-DeepONet 0.12% and FNO 0.12% | Helped |
| Replace linear reconstruction (DeepONet) with nonlinear reconstruction (shift-DeepONet, FNO) | DeepONet on Lax-Sod shock tube · Lax-Sod shock tube | relative median L1 error: DeepONet 4.22% vs shift-DeepONet 2.76% and FNO 1.56%; FCNN 8.83% and ResNet 4.47% | Mixed |
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