# Nonlinear integro-differential operator regression with neural networks

arXiv: https://arxiv.org/abs/1810.08552 · HTML: https://mlsanity.com/paper/1810.08552/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2018.

## Built on by (most cited first, 11 of 11)

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- [GenUQ: Predictive Uncertainty Estimates via Generative Hyper-Networks](https://mlsanity.com/paper/2509.21605/) (2025)
- [Supervised and Unsupervised Neural Network Solver for First Order Hyperbolic Nonlinear PDEs](https://mlsanity.com/paper/2601.06388/) (2026)
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## Abstract (arXiv)

This note introduces a regression technique for finding a class of nonlinear integro-differential operators from data. The method parametrizes the spatial operator with neural networks and Fourier transforms such that it can fit a class of nonlinear operators without needing a library of a priori selected operators. We verify that this method can recover the spatial operators in the fractional heat equation and the Kuramoto-Sivashinsky equation from numerical solutions of the equations.