Dilated convolution neural operator for multiscale partial differential equations

Bo Xu, Lei Zhang

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Keywords: operator learning, multiscale PDE, dilated convolution, high frequency features, spectral bias

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TL;DR: Dilated convolution neural operator for multiscale PDEs.

Abstract:

This paper presents a data-driven operator learning method for multiscale partial differential equations, where preserving high-frequency information is critical. We propose the Dilated Convolution Neural Operator (DCNO), which combines dilated convolution layers to effectively capture high-frequency features at a low computational cost, along with Fourier layers to handle smooth features. We conduct experiments to evaluate the performance of DCNO on various datasets, including the multiscale elliptic equation, its inverse problem, Navier-Stokes equation, and Helmholtz equation. DCNO stands out with significantly higher accuracy compared to existing neural operator techniques, and strikes an optimal balance between accuracy and computational cost.

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Submission Number: 5125