Multi-Level Monte Carlo training of neural operators
File(s)
Published version
Author(s)
Rowbottom, James
Fresca, Stefania
Lio, Pietro
Schönlieb, Carola-Bibiane
Boullé, Nicolas
Type
Journal Article
Abstract
Operator learning is a rapidly growing field that aims to approximate nonlinear operators related to partial differential equations (PDEs) using neural operators. These rely on discretization of input and output functions and are, usually, expensive to train for large-scale problems at
high-resolution. Motivated by this, we present a Multi-Level Monte Carlo (MLMC) approach to train neural operators by leveraging a hierarchy of resolutions of function dicretization. Our framework relies on using gradient corrections from fewer samples of fine-resolution data to decrease the computational cost of training while
maintaining a high level accuracy. The proposed MLMC training procedure can be applied to any architecture accepting multi-resolution data. Our numerical experiments on a range of state-of-the-art models and test-cases
demonstrate improved computational efficiency compared to traditional single-resolution training approaches, and highlight the existence of a Pareto curve between accuracy and computational time, related to the number of samples
per resolution.
high-resolution. Motivated by this, we present a Multi-Level Monte Carlo (MLMC) approach to train neural operators by leveraging a hierarchy of resolutions of function dicretization. Our framework relies on using gradient corrections from fewer samples of fine-resolution data to decrease the computational cost of training while
maintaining a high level accuracy. The proposed MLMC training procedure can be applied to any architecture accepting multi-resolution data. Our numerical experiments on a range of state-of-the-art models and test-cases
demonstrate improved computational efficiency compared to traditional single-resolution training approaches, and highlight the existence of a Pareto curve between accuracy and computational time, related to the number of samples
per resolution.
Date Issued
2026-05-01
Date Acceptance
2026-02-02
Citation
Computer Methods in Applied Mechanics and Engineering, 2026, 453
ISSN
0045-7825
Publisher
Elsevier
Journal / Book Title
Computer Methods in Applied Mechanics and Engineering
Volume
453
Copyright Statement
© 2026 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
http://arxiv.org/abs/2505.12940v1
Subjects
cs.LG
cs.LG
cs.NA
math.NA
Publication Status
Published
Article Number
118800
Date Publish Online
2026-02-10