Frequency domain neural networks for data-driven simulations

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 is configured to operate with decomposed data,
• receive input data for a numerical simulation, the input data expressed in at least a first domain,
• decompose the input data into at least i) low-pass filtered data that captures a low-pass filtered version of the input data in the at least the first domain and ii) high-pass filtered data that captures a high-pass filtered version of the input data in the at least the first domain,
• transform the low-pass filtered data to frequency domain,
• apply a first set of weights to the low-pass filtered data in the frequency domain to generate weighted low-pass filtered data in the frequency domain,
• transform the weighted low-pass filtered data from the frequency domain to the at least the first domain, and
• compose an output for the numerical simulation based on at least the weighted low-pass filtered data in the at least the first domain.

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 for a numerical simulation, the input data expressed in at least a first domain,
• decompose the input data into at least i) low-pass filtered data that captures a low-pass filtered version of the input data in the at least the first domain and ii) high-pass filtered data that captures a high-pass filtered version of the input data in the at least the first domain,
• transform only the low-pass filtered data to frequency domain,
• apply a first set of weights to the low-pass filtered data in the frequency domain to generate weighted low-pass filtered data in the frequency domain,
• transform the weighted low-pass filtered data from the frequency domain to the at least the first domain, and
• compose an output for the numerical simulation based on at least the low-pass filtered data in the at least the first domain.