Leray-Schauder Mappings for Operator Learning
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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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 10 of its 19 references that are in the map. First posted on arXiv 2 Oct 2024.
Builds on
10 of 19 references.
References · 10
- 2018Neural Ordinary Differential Equationscited by 3,733
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
- 2017The Expressive Power of Neural Networks: A View from the Widthcited by 318
- 2022Neural Integral Equationscited by 23
- 2022Neural Integro-Differential Equationscited by 17
- 2023Continuous Spatiotemporal Transformerscited by 7
- 2023Spectral methods for Neural Integral Equationscited by 2
- 2024Projection Methods for Operator Learning and Universal Approximationcited by 2
- 2024Universal Approximation of Operators with Transformers and Neural Integral Operatorscited by 2
Built on by
Citing papers per year: 2026: 1.
1 paper.