mlsanityData to 7 Oct 2026

Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis

arXiv 2503.01036 ↗First posted 2 Mar 2025stat.ML cs.LG cs.NAcited by 6

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Abstract (arXiv)

We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational cost, in terms of training procedures. Our approach is mathematically interpretable and backed by rigorous theoretical guarantees in the form of quantitative worst-case error bounds for the learned equation. Numerical benchmarks demonstrate significant improvements in computational complexity and robustness while achieving one to two orders of magnitude improvements in terms of accuracy compared to state-of-the-art algorithms.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 56 of its 120 references that are in the map. First posted on arXiv 2 Mar 2025.

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56 of 120 references.

References · 56

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38 more
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Cited by year

Citing papers per year: 2025: 6.

6 papers.

  1. 2025Operator Learning at Machine Precisioncited by 6
  2. 2025Bilevel optimization for learning hyperparameters: Application to solving PDEs and inverse problems with Gaussian processescited by 3
  3. 2025A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learningcited by 1
  4. 2025Learning Paths for Dynamic Measure Transport: A Control Perspectivecited by 1
  5. 2025A joint optimization approach to identifying sparse dynamics using least squares kernel collocationcited by 0
  6. 2025Physics-Informed Neural Networks for Joint Source and Parameter Estimation in Advection-Diffusion Equationscited by 0