Rethinking Physics-Informed Regression Beyond Training Loops and Bespoke Architectures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911319492395008 |
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| author | Sabug Jr., Lorenzo Kerrigan, Eric |
| author_facet | Sabug Jr., Lorenzo Kerrigan, Eric |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rethinking Physics-Informed Regression Beyond Training Loops and Bespoke Architectures Sabug Jr., Lorenzo Kerrigan, Eric Optimization and Control Machine Learning 62J02, 62G08 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. |
| title | Rethinking Physics-Informed Regression Beyond Training Loops and Bespoke Architectures |
| topic | Optimization and Control Machine Learning 62J02, 62G08 |
| url | https://arxiv.org/abs/2512.13217 |