Frequency Bias and OOD Generalization in Neural Operators under a Variable-Coefficient Wave Equation

Researchers tested Fourier Neural Operators and DeepONets on a 1D variable-coefficient wave equation under structured out-of-distribution shifts.

Both models were relatively robust to coefficient smoothness shifts, but they behaved differently on frequency shifts.

FNO broke down sharply on unseen high-frequency inputs, while DeepONets degraded more gradually.

The findings highlight that strong in-distribution results do not guarantee robustness for neural PDE solvers under shifted inputs.