2025/12/15 by Lorenzo Sabug, Eric C. Kerrigan, Sabug, Lorenzo +1
Physics and Astronomy · Materials Science · Computer Science · #Model Reduction and Neural Networks #Machine Learning in Materials Science #Neural Networks and Reservoir Computing
paper · pdf · doi:10.48550/arxiv.2512.13217
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.