# Leray-Schauder Mappings for Operator Learning

arXiv: https://arxiv.org/abs/2410.01746 · HTML: https://mlsanity.com/paper/2410.01746/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 10 of 10)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Neural Integral Equations](https://mlsanity.com/paper/2209.15190/) (2022)
- [Neural Integro-Differential Equations](https://mlsanity.com/paper/2206.14282/) (2022)
- [Continuous Spatiotemporal Transformers](https://mlsanity.com/paper/2301.13338/) (2023)
- [Spectral methods for Neural Integral Equations](https://mlsanity.com/paper/2312.05654/) (2023)
- [Projection Methods for Operator Learning and Universal Approximation](https://mlsanity.com/paper/2406.12264/) (2024)
- [Universal Approximation of Operators with Transformers and Neural Integral Operators](https://mlsanity.com/paper/2409.00841/) (2024)

## Built on by (most cited first, 1 of 1)

- [Universal Approximation of Nonlinear Operators and Their Derivatives](https://mlsanity.com/paper/2605.15285/) (2026)

## Abstract (arXiv)

We present an algorithm for learning operators between Banach spaces, based on the use of Leray-Schauder mappings to learn a finite-dimensional approximation of compact subspaces. We show that the resulting method is a universal approximator of (possibly nonlinear) operators. We demonstrate the efficiency of the approach on two benchmark datasets showing it achieves results comparable to state of the art models.