Gaussian Processes and Bayesian Inference
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Abstract
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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@article{Guo2026unified,
title = {A unified perspective of Gaussian process approximation for differential equations},
author = {Mengwu Guo},
journal = {arXiv (Cornell University)},
year = {2026},
doi = {10.48550/arxiv.2607.06292},
url = {https://doi.org/10.48550/arxiv.2607.06292}
}FAQ
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