Fourier neural operator networks with sub-sampled non-linear transformations

A system, comprising:

• one or more computer readable storage media;
• and
• program instructions stored on the one or more computer readable storage media that, when executed by at least one processor, cause the at least one processor to:
• receive training data for training a neural network to perform numerical simulations to model a physical phenomenon, the training data determined based on a solution of one or more differential equations that model the physical phenomenon,
• train a neural network, based on the training data, to perform numerical simulations modeling the physical phenomenon, wherein the neural network includes multiple frequency domain stages configured to apply non-linear transformations to sub-sampled input data in frequency domain;
• receive input data for a numerical simulation, the input data expressed in at least a first domain;
• transform the input data from the first domain to frequency domain, including generating a plurality of frequency modes of the input data in the frequency domain;
• down-sample the plurality of frequency modes to generate down-sampled input data in the frequency domain, the down-sampled input data including a subset of the plurality of frequency modes;
• successively process the down-sampled input data with the multiple stages of the neural network to generate a down-sampled output in the frequency domain, the processing including applying, in each stage of the multiple stages, the non-linear transformation to the subset of the plurality of frequency modes;
• up-sample the down-sampled output to generate an up-sampled output corresponding to the plurality of frequency modes in the frequency domain;
• and
• transform the up-sampled output from the frequency domain to the at least the first domain to generate a result of the numerical simulation.

A computer-readable storage medium storing computer-executable instructions that when executed by at least one processor cause a computer system to:

• receive input data expressed in at least a first domain;
• transform the input data from the first domain to frequency domain, including generating a plurality of frequency modes of the input data in the frequency domain;
• down-sample the plurality of frequency modes to generate down-sampled input data in the frequency domain, the down-sampled input data including a subset of the plurality of frequency modes;
• successively process the down-sampled input data with one or more stages of a neural network to generate a down-sampled output in the frequency domain, the processing including applying, in each stage of the one or more stages, a non-linear transformation to the subset of the plurality of frequency modes;
• up-sample the down-sampled output to generate an up-sampled output corresponding to the plurality of frequency modes in the frequency domain;
• and
• transform the up-sampled output from the frequency domain to the at least the first domain to generate a result of the numerical simulation.