Physics-Informed Regression: Parameter Estimation in Parameter-Linear Nonlinear Dynamic Models
物理信息回归：参数线性非线性动力模型的参数估计AI 解读 ↓
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物理信息回归：参数线性非线性动力模型的参数估计
- 研究问题
- 作者研究当非线性动力方程对未知参数保持线性时，能否用回归高效估计参数，并与物理信息神经网络比较表现和计算速度。
- 方法与思路
- 作者将参数线性的常微分和偏微分方程转化为正则化 OLS 估计问题，在合成数据及丹麦疫情时间序列上分析固定和时变参数。
- 材料陈述的贡献
- 摘要称，两种方法均能估计目标参数，但所考察模型中物理信息回归的表现和速度更好，复杂分舱模型的比较尤其支持该方法。
- 阅读关注点
- 应核对如何由观测构造方程回归量、导数近似与噪声处理、正则化选择，以及两类方法比较时的精度和计算预算是否一致。
- 阅读边界
- 依据 arXiv 预印本摘要，同行评审或期刊接收未核实；优势限于摘要所述模型，未说明一般统计保证，不能推广至非参数线性系统。
原文摘要
We present a new efficient hybrid parameter estimation method based on the idea, that if nonlinear dynamic models are stated in terms of a system of equations that is linear in terms of the parameters, then regularized ordinary least squares can be used to estimate these parameters from time series data. We introduce the term "Physics-Informed Regression" (PIR) to describe the proposed data-driven hybrid technique as a way to bridge theory and data by use of ordinary least squares to efficiently perform parameter estimation of the model coefficients of different parameter-linear models; providing examples of models based on nonlinear ordinary equations (ODE) and partial differential equations (PDE). The focus is on parameter estimation on a selection of ODE and PDE models, each illustrating performance in different model characteristics. For two relevant epidemic models of different complexity and number of parameters, PIR is tested and compared against the related technique, physics-informed neural networks (PINN), both on synthetic data generated from known target parameters and on real public Danish time series data collected during the COVID-19 pandemic in Denmark. Both methods were able to estimate the target parameters, while PIR showed to perform noticeably better, especially on a compartment model with higher complexity. Given the difference in computational speed, it is concluded that the PIR method is superior to PINN for the models considered. It is also demonstrated how PIR can be applied to estimate the time-varying parameters of a compartment model that is fitted using real Danish data from the COVID-19 pandemic obtained during a period from 2020 to 2021. The study shows how data-driven and physics-informed techniques may support reliable and fast -- possibly real-time -- parameter estimation in parameter-linear nonlinear dynamic models.