# BCR-Net: a neural network based on the nonstandard wavelet form

arXiv: https://arxiv.org/abs/1810.08754 · HTML: https://mlsanity.com/paper/1810.08754/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2018.

## Built on by (most cited first, 18 of 18)

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- [Approximation of Solution Operators for High-dimensional PDEs](https://mlsanity.com/paper/2401.10385/) (2024)
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## Abstract (arXiv)

This paper proposes a novel neural network architecture inspired by the nonstandard form proposed by Beylkin, Coifman, and Rokhlin in [Communications on Pure and Applied Mathematics, 44(2), 141-183]. The nonstandard form is a highly effective wavelet-based compression scheme for linear integral operators. In this work, we first represent the matrix-vector product algorithm of the nonstandard form as a linear neural network where every scale of the multiresolution computation is carried out by a locally connected linear sub-network. In order to address nonlinear problems, we propose an extension, called BCR-Net, by replacing each linear sub-network with a deeper and more powerful nonlinear one. Numerical results demonstrate the efficiency of the new architecture by approximating nonlinear maps that arise in homogenization theory and stochastic computation.