论文标题
从具有隐藏变量的数据中发现微分方程
Uncovering differential equations from data with hidden variables
论文作者
论文摘要
辛迪（Sindy）是一种通过解决稀疏线性回归优化问题来学习从数据学习微分方程的方法[Brunton等，2016]。在本文中，我们提出了Sindy方法的扩展，该方法在未观察到某些变量的情况下学习微分方程的系统。我们的延伸是基于将目标变量的高阶时间导数回归到函数字典上，该函数包括目标变量的较低阶段衍生物。我们通过测量学习动力学系统对合成数据的预测准确性以及由Réseaudede te Transportd'électricité（RTE）提供的实际数据集的预测准确性。我们的方法提供了高质量的短期预测，并且比学习具有潜在变量的微分方程的竞争方法要快。
SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton et al., 2016]. 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 (RTE). 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.
