{"ID":6023587,"CreatedAt":"2026-07-08T01:00:23.257252134Z","UpdatedAt":"2026-07-10T13:53:55.553307773Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.06292","arxiv_id":"2607.06292","title":"A unified perspective of Gaussian process approximation for differential equations","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.","short_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 interpretat...","url_abs":"https://arxiv.org/abs/2607.06292","url_pdf":"https://arxiv.org/pdf/2607.06292v1","authors":"[\"Mengwu Guo\"]","published":"2026-07-07T14:00:44Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"cs.CE\",\"stat.ML\"]","methods":"[]","has_code":false}