论文标题
关于回归和贝叶斯方法的观点，用于系统识别模式形成动力学的观点
A Perspective on Regression and Bayesian Approaches for System Identification of Pattern Formation Dynamics
论文作者
论文摘要
我们提供了两种用于系统识别的方法，即从测量数据中识别部分微分方程（PDE）。第一个是一个基于回归的变分系统识别过程，它在不需要重复的远期模型求解并且对大量差分运算符具有良好的可扩展性方面是有利的。但是，它具有严格的数据类型要求，需要通过可用数据直接代表操作员的能力。第二个是贝叶斯推理框架，对于提供不确定性量化非常有价值，并且可以灵活地容纳可能是间接关注数量的稀疏和嘈杂数据。但是，它还需要昂贵的PDE模型的重复前向解决方案，并阻碍可扩展性。我们为模型形成动力学的模型问题提供了结果，并讨论了提出的方法的优点。
We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in not requiring repeated forward model solves and has good scalability to large number of differential operators. However it has strict data type requirements needing the ability to directly represent the operators through the available data. The second is a Bayesian inference framework highly valuable for providing uncertainty quantification, and flexible for accommodating sparse and noisy data that may also be indirect quantities of interest. However, it also requires repeated forward solutions of the PDE models which is expensive and hinders scalability. We provide illustrations of results on a model problem for pattern formation dynamics, and discuss merits of the presented methods.
