GIT-Net: Generalized Integral Transform for Operator Learning
This work addresses the challenge of efficient and accurate neural network operators for PDEs, offering a generalized approach that balances performance and computational demands, though it appears incremental in improving upon existing methods.
The paper tackles the problem of approximating Partial Differential Equation (PDE) operators by introducing GIT-Net, a deep neural network architecture inspired by integral transforms, which achieves competitive performance with small test errors and low computational costs across various PDE problems.
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.