Physics-Informed Basis Functions for Nonlinear Response Curve Decomposition: A Parsimonious Alternative to Splines
Abstract
Curve fitting for physical, biological, and engineering data typically forces a choice between interpretable but rigid parametric forms and flexible but physically opaque smoothers. This paper introduces the Growth-Decay Curve (GDC), a physics-informed basis derived as the product of a lognormal growth cumulative distribution function and an exponential decay term, each traceable to a governing differential equation. GDC's parameters correspond directly to growth and decay timescales, yielding dimensionless ratios and shape descriptors that connect the fit back to the underlying dynamics. Across simulated differential-equation solutions and applications spanning physical, biological, and economic data, GDC matches the fit quality of splines, generalized additive models, radial basis function networks, and Fourier regression, while remaining substantially more parsimonious and physically interpretable.
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BibTeX
@misc{kunz2026physicsinformed,
title = {{Physics-Informed Basis Functions for Nonlinear Response Curve Decomposition: A Parsimonious Alternative to Splines}},
author = {M. Ross Kunz and Jieun Lee and Jaden Palmer},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28870},
eprint = {2608.28870},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28870},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Physics-Informed Basis Functions for Nonlinear Response Curve Decomposition: A Parsimonious Alternative to Splines
AU - M. Ross Kunz
AU - Jieun Lee
AU - Jaden Palmer
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28870
UR - https://arxiv.org/abs/2608.28870
AB - Curve fitting for physical, biological, and engineering data typically forces a choice between interpretable but rigid parametric forms and flexible but physically opaque smoothers. This paper introduces the Growth-Decay Curve (GDC), a physics-informed basis derived as the product of a lognormal growth cumulative distribution function and an exponential decay term, each traceable to a governing differential equation. GDC's parameters correspond directly to growth and decay timescales, yielding dimensionless ratios and shape descriptors that connect the fit back to the underlying dynamics. Across simulated differential-equation solutions and applications spanning physical, biological, and economic data, GDC matches the fit quality of splines, generalized additive models, radial basis function networks, and Fourier regression, while remaining substantially more parsimonious and physically interpretable.
ER -