Somacal Agustín, Barrera Yamila, Boechi Leonardo, Jonckheere Matthieu, Lefieux Vincent, Picard Dominique, Smucler Ezequiel
Aristas S.R.L., Dorrego 1940, Torre A, 2do Piso, dpto. N (1425), Ciudad Autónoma de Buenos Aires, Argentina.
Instituto de Calculo-CONICET, Intendente Güiraldes 2160, Ciudad Universitaria, Pabellón II, 2do. piso, (C1428EGA), Buenos Aires, Argentina.
Phys Rev E. 2022 May;105(5-1):054209. doi: 10.1103/PhysRevE.105.054209.
SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton, Proctor, and Kutz, Proc. Natl. Acad. Sci. USA 113, 3932 (2016)PNASA60027-842410.1073/pnas.1517384113]. In this article, we propose an extension of the SINDy method that learns systems of differential equations in cases where some of the variables are not observed. Our extension is based on regressing a higher order time derivative of a target variable onto a dictionary of functions that includes lower order time derivatives of the target variable. We evaluate our method by measuring the prediction accuracy of the learned dynamical systems on synthetic data and on a real data set of temperature time series provided by the Réseau de Transport d'Électricité. Our method provides high quality short-term forecasts and it is orders of magnitude faster than competing methods for learning differential equations with latent variables.
SINDy是一种通过求解稀疏线性回归优化问题从数据中学习微分方程系统的方法[Brunton、Proctor和Kutz，《美国国家科学院院刊》113, 3932 (2016)PNASA60027 - 842410.1073/pnas.1517384113]。在本文中，我们提出了SINDy方法的一种扩展，该扩展方法可在某些变量未被观测到的情况下学习微分方程系统。我们的扩展基于将目标变量的高阶时间导数回归到一个函数字典上，该字典包括目标变量的低阶时间导数。我们通过测量所学习的动力系统对合成数据以及由法国电力传输网络提供的温度时间序列真实数据集的预测准确性来评估我们的方法。我们的方法提供了高质量的短期预测，并且比用于学习带有潜在变量的微分方程的竞争方法快几个数量级。
