🤖 AI Summary
本文提出了一种基于物理信息的基函数（GDC），用于非线性响应曲线分解，解决了传统方法在解释性和灵活性之间的权衡问题。
📝 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.