Isotropic Fourier Neural Operators
For researchers using neural operators to solve PDEs, this work provides a principled way to incorporate physical symmetries, improving efficiency and accuracy.
The authors propose Isotropic Fourier Neural Operators, a modification to Fourier Neural Operators that enforces spatial symmetries (isotropy), improving model performance and reducing parameters by up to 16x in 2D and 96x in 3D.
Fourier Neural Operators are deep learning models that learn mappings between function spaces and can be used to learn and solve partial differential equations (PDEs), in some cases significantly faster than traditional PDE solvers. Within the model are Fourier layers, which apply linear transformations directly to the Fourier modes, with parameters depending on the wave numbers. However, most physical systems are isotropic, with the results being independent of the coordinate system chosen, but the linear transformations do not necessarily respect these symmetries. We propose a modification to the linear transformations that ensures spatial symmetries are respected, called the Isotropic Fourier Neural Operator, which both improves model performance and reduces the number of parameters by up to a factor of 16 in 2D and 96 in 3D.