A Structured Matrix Method for Nonequispaced Neural Operators
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Publication:6438621
arXiv2305.19663MaRDI QIDQ6438621
Author name not available (Why is that?)
Publication date: 31 May 2023
Abstract: Fourier Neural Operators (FNOs) have emerged as very popular machine learning architectures for learning operators, particularly those arising in PDEs. However, as FNOs rely on the fast Fourier transform for computational efficiency, the architecture can be limited to input data on equispaced Cartesian grids. Here, we generalize FNOs to handle input data on non-equispaced point distributions. Our proposed model, termed as Vandermonde Neural Operator (VNO), utilizes Vandermonde-structured matrices to efficiently compute forward and inverse Fourier transforms, even on arbitrarily distributed points. We present numerical experiments to demonstrate that VNOs can be significantly faster than FNOs, while retaining comparable accuracy, and improve upon accuracy of comparable non-equispaced methods such as the Geo-FNO.
Has companion code repository: https://github.com/camlab-ethz/dse-for-neuraloperators
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