发表机构
Idaho National Laboratory（爱达荷国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出物理信息基函数GDC，其拟合质量与多种常用曲线拟合方法相当，兼具高简约性与物理可解释性，可替代样条用于多领域数据的曲线分解。
AI 中文摘要
针对物理、生物及工程数据的曲线拟合，通常需在可解释但刚性的参数形式与灵活但物理意义模糊的平滑器间做选择。本文提出增长-衰减曲线（Growth-Decay Curve, GDC），这是一种物理信息基函数，由对数正态增长累积分布函数与指数衰减项的乘积推导而来，两者均可追溯至控制微分方程。GDC的参数直接对应增长与衰减时间尺度，产生无量纲比率与形状描述符，将拟合结果与底层动力学关联。在模拟微分方程解及涵盖物理、生物、经济数据的应用中，GDC的拟合质量可与样条、广义加性模型、径向基函数网络及傅里叶回归相媲美，同时保持显著更高的简约性与物理可解释性。
英文摘要
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.
