A unified perspective of Gaussian process approximation for differential equations

• URL: http://arxiv.org/abs/2607.06292v1
• Date: Tue, 07 Jul 2026 14:00:44 GMT
• Title: A unified perspective of Gaussian process approximation for differential equations
• Abstract summary: We present a unified Bayesian perspective that places these techniques within a common probabilistic framework.<n>This work aims to consolidate current developments and provide a foundation for future research.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The use of Gaussian processes for approximating differential equations has expanded rapidly, leading to a growing, diverse, and fragmented body of numerical methods. We present a unified Bayesian perspective that places these techniques within a common probabilistic framework, based on a derivative matching interpretation for incorporating differential equation constraints into likelihood. This unified perspective supports both parameter estimation and solution approximation, and shows how a range of existing methods can be understood within it. This work aims to consolidate current developments and provide a foundation for future research.

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