Dimensionally consistent surrogate modelling through dimensional analysis and harmonic expansions
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 Π-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.
Versions
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BibTeX
@misc{tarrus2026dimensionally,
title = {{Dimensionally consistent surrogate modelling through dimensional analysis and harmonic expansions}},
author = {Ernest Tarrus and Hector Gisbert},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38094},
eprint = {2609.38094},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38094},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dimensionally consistent surrogate modelling through dimensional analysis and harmonic expansions
AU - Ernest Tarrus
AU - Hector Gisbert
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38094
UR - https://arxiv.org/abs/2609.38094
AB - 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 Π-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.
ER -