Resolution-Invariant Image Classification based on Fourier Neural Operators

arXiv2304.01227MaRDI QIDQ6431918

Samira Kabri, Daniel Tenbrinck, Tim Roith, Martin Burger

Publication date: 2 April 2023

Abstract: In this paper we investigate the use of Fourier Neural Operators (FNOs) for image classification in comparison to standard Convolutional Neural Networks (CNNs). Neural operators are a discretization-invariant generalization of neural networks to approximate operators between infinite dimensional function spaces. FNOs - which are neural operators with a specific parametrization - have been applied successfully in the context of parametric PDEs. We derive the FNO architecture as an example for continuous and Fr'echet-differentiable neural operators on Lebesgue spaces. We further show how CNNs can be converted into FNOs and vice versa and propose an interpolation-equivariant adaptation of the architecture.

Has companion code repository: https://github.com/samirak98/fourierimaging

Mathematics Subject Classification ID

Numerical methods for trigonometric approximation and interpolation (65T40) Machine vision and scene understanding (68T45)

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