{"ID":2828914,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.13217","arxiv_id":"2512.13217","title":"Rethinking Physics-Informed Regression Beyond Training Loops and Bespoke Architectures","abstract":"We revisit the problem of physics-informed regression, and propose a method that directly computes the state at the prediction point, simultaneously with the derivative and curvature information of the existing samples. We frame each prediction as a constrained optimisation problem, leveraging multivariate Taylor series expansions and explicitly enforcing physical laws. Each individual query can be processed with low computational cost without any pre- or re-training, in contrast to global function approximator-based solutions such as neural networks. Our comparative benchmarks on a reaction-diffusion system show competitive predictive accuracy relative to a neural network-based solution, while completely eliminating the need for long training loops, and remaining robust to changes in the sampling layout.","short_abstract":"We revisit the problem of physics-informed regression, and propose a method that directly computes the state at the prediction point, simultaneously with the derivative and curvature information of the existing samples. We frame each prediction as a constrained optimisation problem, leveraging multivariate Taylor serie...","url_abs":"https://arxiv.org/abs/2512.13217","url_pdf":"https://arxiv.org/pdf/2512.13217v1","authors":"[\"Lorenzo Sabug\",\"Eric Kerrigan\"]","published":"2025-12-15T11:31:41Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\"]","methods":"[\"Diffusion Model\"]","has_code":false}