HyperFNO: Improving the Generalization Behavior of Fourier Neural Operators

Physic-informed machine learning aims to build surrogate models for real-world physical systems governed by partial differentiable equations (PDEs). One of the more popular recently proposed approaches is the Fourier Neural Operator (FNO), which learns the Green's function operator for PDEs based only on observational data. These operators are able to model PDEs for a variety of initial conditions and show the ability of multi-scale prediction. % However, as we will show, this model class is not able to model a high variation of the parameters of some PDEs.However, as we will show, this model class is not able to generalize to changes in the parameters of the PDEs, such as the viscosity coefficient or forcing term.We propose HyperFNO, an approach combining FNOs with hypernetworks so as to improve the models' extrapolation behavior to a wider range of PDE parameters using a single model. HyperFNO learns to generate the parameters of functions operating in both the original and the frequency domain. The proposed architecture is evaluated using various simulation problems.