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Fourier Neural Operator with Learned Deformations for PDEs on General Geometries

Journal of machine learning research, 2022
Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a variety of PDEs ...
Zong-Yi Li   +3 more
semanticscholar   +1 more source

On Fourier Series on the Torus and Fourier Transforms

Mathematical Notes, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Representation of the Fourier Transform by Fourier Series

Journal of Mathematical Imaging and Vision, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fourier series and Fourier transforms

2013
Some of the most versatile mathematical functions are the trigonometric functions sine and cosine. As a result, it is often very helpful to express a general function as a linear combination of these functions and then to carry out manipulations on the resulting series.
Peter Atkins   +2 more
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Fourier Series and Fourier Transforms

2003
In Chapter 3, we touched upon the analogy between the diffraction of x-rays and that of visible light. Here, we extend that discussion and consider some aspects of Fourier series and Fourier transforms.
Mark Ladd, Rex Palmer
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Fourier matrices and Fourier tensors

Frontiers of Mathematics in China, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fourier microfluidics

Lab on a Chip, 2008
We present a new experimental technique for the separation of dynamic chemical signals based on their frequency domain characteristics. Such a technique can be used to create filters that separate slow signals from fast signals from a common input flow stream.
Y, Xie   +3 more
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Fourier Series and Fourier Transform

1998
In this chapter we look at some of the eigenfunction expansions in terms of Fourier series. We develop the Fourier transform and use it to solve the heat equation again. We also give a brief treatment of the discrete Fourier transform (DFT) and the fast Fourier transform (FFT).
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