Fourier Neural Operator
A neural operator model proposed by Zongyi Li et al. in 2020 that learns operator mappings in the frequency domain to solve partial differential equations. The architecture is characterized by the ability to capture long-range dependencies and exhibits resolution invariance.
Core Facts
Timeline (last 90 days)
Neural operators are a class of deep learning models that learn mappings between infinite-dimensional function spaces, aiming to approximate the solution operator of PDEs, are resolution-independent, and representative architectures include FNO and DeepONet.
The paper's system consists of four modules: a global Fourier Neural Operator, a local operator, a set-aware selector, and a macro policy.
FNO transforms the input function to frequency space via Fast Fourier Transform, applies a learnable linear transformation to the low-frequency components, and then transforms back to the spatial domain via inverse FFT.
FNO has resolution invariance: it can be trained on low-resolution grids and directly transferred to finer grids at inference time.
All Facts (4)
Neural operators are a class of deep learning models that learn mappings between infinite-dimensional function spaces, aiming to approximate the solution operator of PDEs, are resolution-independent, and representative architectures include FNO and DeepONet.
75%UnverifiedThe paper's system consists of four modules: a global Fourier Neural Operator, a local operator, a set-aware selector, and a macro policy.
50%UnverifiedFNO transforms the input function to frequency space via Fast Fourier Transform, applies a learnable linear transformation to the low-frequency components, and then transforms back to the spatial domain via inverse FFT.
50%UnverifiedFNO has resolution invariance: it can be trained on low-resolution grids and directly transferred to finer grids at inference time.
50%