Gaussian Process Regression for Inverse Problems in Linear PDEs

• URL: http://arxiv.org/abs/2502.04276v1
• Date: Thu, 06 Feb 2025 18:20:38 GMT
• Title: Gaussian Process Regression for Inverse Problems in Linear PDEs
• Authors: Xin Li, Markus Lange-Hegermann, Bogdan Raiţă,
• Abstract summary: This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs) An example application includes identifying the wave speed from noisy data for classical wave equations, which are widely used in physics.
• Score: 7.793266750812356
• License:
• Abstract: 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.

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