Rethinking Physics-Informed Regression Beyond Training Loops and Bespoke Architectures

• URL: http://arxiv.org/abs/2512.13217v1
• Date: Mon, 15 Dec 2025 11:31:41 GMT
• Title: Rethinking Physics-Informed Regression Beyond Training Loops and Bespoke Architectures
• Authors: Lorenzo Sabug, Eric Kerrigan,
• Abstract summary: We propose a method that computes the state at the prediction point, simultaneously with the derivative and curvature information of the existing samples.<n>Each 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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