GIT-Net: Generalized Integral Transform for Operator Learning
Chao Wang Alexandre Hoang Thiery
This article introduces GIT-Net, a deep neural network architecture for
approximating Partial Differential Equation (PDE) operators, inspired by
integral transform operators. GIT-NET harnesses the fact that differential
operators commonly used for defining PDEs can often be represented
parsimoniously when expressed in specialized functional bases (e.g., Fourier
basis). Unlike rigid integral transforms, GIT-Net parametrizes adaptive
generalized integral transforms with deep neural networks. When compared to
several recently proposed alternatives, GIT-Net's computational and memory
requirements scale gracefully with mesh discretizations, facilitating its
application to PDE problems on complex geometries. Numerical experiments
demonstrate that GIT-Net is a competitive neural network operator, exhibiting
small test errors and low evaluations across a range of PDE problems. This
stands in contrast to existing neural network operators, which typically excel
in just one of these areas.