Gaussian Process Regression for Inverse Problems in Linear PDEs
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Abstract (arXiv)
This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors defined based on advanced commutative algebra and algebraic analysis. The implementation of these priors is algorithmic and achieved using the Macaulay2 computer algebra software. An example application includes identifying the wave speed from noisy data for classical wave equations, which are widely used in physics. The method achieves high accuracy while enhancing computational efficiency.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 6 of its 15 references that are in the map. First posted on arXiv 6 Feb 2025.
Builds on
6 of 15 references.
References · 6
- 2017Machine Learning of Linear Differential Equations using Gaussian Processescited by 139
- 2018Algorithmic Linearly Constrained Gaussian Processescited by 20
- 2022Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficientscited by 17
- 2022Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equationscited by 14
- 2023Gaussian processes for Bayesian inverse problems associated with linear partial differential equationscited by 9
- 2018PDE-constrained optimization in medical image analysiscited by 5
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Citing papers per year: 2025: 1; 2026: 1.
2 papers.