[
    {
        "id": "osp-21695",
        "type": "article-journal",
        "title": "Dimensionally consistent surrogate modelling through dimensional analysis and harmonic expansions",
        "author": [
            {
                "family": "Tarrus",
                "given": "Ernest"
            },
            {
                "family": "Gisbert",
                "given": "Hector"
            }
        ],
        "URL": "https://omanscience.com/en/articles/dimensionally-consistent-surrogate-modelling-through-dimensional-analysis-and-harmonic-expansions",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "DOI": "10.1038/s41598-026-63672-z",
        "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."
    }
]