aiqbench analysis
This research introduces a data-driven framework for constructing surrogate models that strictly adhere to dimensional homogeneity, a fundamental requirement for physically meaningful equations. By combining Buckingham $\Pi$-groups with harmonic expansions and regularized linear regression, the method improves conditioning and sample efficiency compared to standard unconstrained baselines. The approach is validated across diverse physical systems, from classical mechanics to black-body radiation spectra, offering explicit and computationally inexpensive models for structured scientific problems.
Dimensionally consistent surrogate modelling through dimensional analysis and harmonic expansions
arXiv:2609.38094v1 Announce Type: new Abstract: Dimensional homogeneity is a fundamental constraint on physically meaningful models, requiring invariance under changes of units. We present a data-driven method for constructing surrogate models that satisfy this constraint at the level of the hypothesis class. Starting from a dimension matrix of measured variables, the method derives Buckingham $\Pi$-groups, constructs admissible dimensional prefactors, and approximates the remaining dimensionless dependence using truncated harmonic expansions on normalized invariant domains. Once the prefactor and dictionary are fixed, the coefficients are obtained from a regularized linear regression problem. We test the approach on the simple pendulum, Planck's black-body law, the double-pendulum Lyapunov field, and an experimental COBE/FIRAS black-body spectrum dataset. The results show that dimensional constraints improve conditioning, robustness to noise, and sample efficiency relative to unconstrained baselines, while the choice of dictionary becomes important in non-periodic or multi-invariant settings. The learned expressions are explicit and inexpensive to evaluate, which makes them useful as surrogate models for structured physical problems.
Abstract:Dimensional homogeneity is a fundamental constraint on physically meaningful models, requiring invariance under changes of units. We present a data-driven method for constructing surrogate models that satisfy this constraint at the level of the hypothesis class. Starting from a dimension matrix of measured variables, the method derives Buckingham $\Pi$-groups, constructs admissible dimensional prefactors, and approximates the remaining dimensionless dependence using truncated harmonic expansions on normalized invariant domains. Once the prefactor and dictionary are fixed, the coefficients are obtained from a regularized linear regression problem. We test the approach on the simple pendulum, Planck's black-body law, the double-pendulum Lyapunov field, and an experimental COBE/FIRAS black-body spectrum dataset. The results show that dimensional constraints improve conditioning, robustness to noise, and sample efficiency relative to unconstrained baselines, while the choice of dictionary becomes important in non-periodic or multi-invariant settings. The learned expressions are explicit and inexpensive to evaluate, which makes them useful as surrogate models for structured physical problems.
45 pages, 15 figures. Published in Scientific Reports
Machine Learning (cs.LG); High Energy Physics - Phenomenology (hep-ph)
arXiv:2609.38094 [cs.LG]
(or arXiv:2609.38094v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.38094 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
Sci. Rep. (2026)
https://doi.org/10.1038/s41598-026-63672-z Focus to learn more DOI(s) linking to related resources
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 277 words
Related coverage
Adaptive surrogate modeling for high-dimensional spatio-temporal output
arXiv · Aug 20, 2026
Cycle-Consistent and Uncertainty-Aware Neural Surrogates for Tokamak Edge Plasmas
arXiv · Jul 24, 2026
Structured Extrema Errors in Classical Surrogates for Viscous Burgers: A Physics-Consistent Interpretation
arXiv · Sep 9, 2026
Deterministic World Models for Closed-loop Reachability Analysis of End-to-End Vision-based Control
arXiv · Aug 7, 2026