Rotation Equivariant Fourier Neural Operators for Learning Symmetry Preserving Transformations on Scalar Fields, Vector Fields, and Higher Order Tensor Fields
Year: 2021
Type: preprint
Abstract: We introduce equivariant neural operators for learning resolution invariant, rotation equivariant and consequently symmetry preserving transformations between arbitrary sets of tensor fields including scalar fields, vector fields, and higher order fields. Our tensor field convolution layers emulate any linear operator by learning its impulse response or Green's function as the convolution kernel. Our tensor field attention layers emulate pairwise field coupling via local tensor products. Convolutions and associated adjoints can be in real or Fourier space allowing for linear scaling. By unifying concepts from Euclidean tensor field networks (E3NN), tensor basis networks (TBNN) and Fourier neural operators (FNO), we achieve good predictive performance on a wide range of PDEs and dynamical systems in engineering and quantum chemistry. Code is in Julia and available upon request from authors.
Source: arXiv (Cornell University)
Institutions: Carnegie Mellon University, RWTH Aachen University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3203019825