mlsanityData to 7 Oct 2026

Multi-Level Monte Carlo Training of Neural Operators

arXiv 2505.12940 ↗First posted 19 May 2025cs.LG cs.NA math.NAcited by 4

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Abstract (arXiv)

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 discretization. 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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 28 of its 45 references that are in the map. First posted on arXiv 19 May 2025.

Builds on

28 of 45 references.

References · 28

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16 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Operator Learning Using Weak Supervision from Walk-on-Spherescited by 1
  2. 2026A meshfree exterior calculus for generalizable and data-efficient learning of physics from point cloudscited by 1
  3. 2026Multi-Fidelity SINDy: Sparse Discovery of Nonlinear Dynamical Systems with Fidelity-Weighted Measurementscited by 1
  4. 2026A neural operator view on U-Nets for inverse imaging problemscited by 0