Authors: Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar (Caltech & Purdue University) · arXiv: 2010.08895
Parameterizes the global integral kernel operator in Fourier frequency space via Fast Fourier Transform (FFT), achieving discretization-invariant zero-shot super-resolution on Burgers, Darcy Flow, and Navier-Stokes PDEs up to 1000x faster than traditional numerical solvers.
Key Quantitative & Theoretical Takeaway: By truncating to k_max low-frequency Fourier modes and combining spectral convolution with a local linear bypass W, FNO learns resolution-independent operators between infinite-dimensional function spaces.
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. We formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture.
Because the learned weight tensor R_phi acts on low-frequency Fourier modes k <= k_max in continuous frequency space rather than fixed spatial grid stencils, the same parameters can be evaluated on any spatial resolution via FFT and inverse FFT.
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