论文标题
时空数据驱动的动态方程发现的贝叶斯方法发现
A Bayesian Approach for Spatio-Temporal Data-Driven Dynamic Equation Discovery
论文作者
论文摘要
基于物理原理的微分方程用于代表科学和工程所有领域的复杂动态系统。通过在学术界和行业中反复使用，这些方程式已证明可以很好地代表现实世界的动态。由于这些复杂系统的真实动态通常是未知的，因此学习管理方程式可以提高我们对驱动系统机制的理解。在这里，我们开发了一种贝叶斯方法，以发现非线性时空动态方程的数据驱动。我们的方法可以容纳测量噪声和缺少数据，这两者在现实世界中很常见，并且说明了参数不确定性。使用三个模拟系统说明了所提出的框架，该系统具有不同数量的观察不确定性和缺失数据，并应用于现实世界系统以推断流函数涡度的时间演变。
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent real-world dynamics well. Since the true dynamics of these complex systems are generally unknown, learning the governing equations can improve our understanding of the mechanisms driving the systems. Here, we develop a Bayesian approach to data-driven discovery of non-linear spatio-temporal dynamic equations. Our approach can accommodate measurement noise and missing data, both of which are common in real-world data, and accounts for parameter uncertainty. The proposed framework is illustrated using three simulated systems with varying amounts of observational uncertainty and missing data and applied to a real-world system to infer the temporal evolution of the vorticity of the streamfunction.
