Data-driven model order reduction

本研究的目的是为时变、非线性和多维动力系统提供直接从数据（数据驱动模型降阶）简化模型的突破性进展。时变和非线性现象在物理和工程（例如MEMS， VLSI电路，智能电网，机器人，汽车和航空航天工程，分子生物学，仅举几例）中占主导地位，因此这项研究将在几个领域具有广泛的应用。通常的模型降阶方法包括假设一组包含未指定参数的方程，这些参数将拟合到数据中。方程参数的性质和数量取决于对模型的洞察，或者通过数学上的假设来实现对测量的某种解释。这里提出的研究的概念基础是让数据自己说话。我们的目标是提供（降阶）建模过程，从系统上尽可能小的假设集开始，直接为它构建数学模型。事实上，关于系统的唯一假设是系统变量之间存在平衡关系，涉及测量量（例如输入和输出）和系统状态。

The purpose of this research is to provide ground-breaking advances in the simplification of models directly from data (data-driven model order reduction) for the classes of time-varying, of nonlinear, and of multidimensional dynamical systems. Time-varying and nonlinear phenomena are predominant in physics and engineering (e.g. in MEMS, VLSI circuits, smart grids, robotics, automotive and aerospace engineering, molecular biology, to name but afew), and consequently this research will have wide application in several areas. The usual approach to model order reduction consists in postulating a set of equations containing unspecified parameters that are to be fitted to the data. The nature and quantity of the equation parameters is determined by insight into the model, or by assumptions that are mathematically instrumental to achieve some explanation for the measurements. The conceptual foundation of the research proposed here is instead to let the data speak foritself. We aim to provide (reduced-order) modelling procedures that starting from the smallest possible set of assumptions on the system, directly construct mathematical models for it. In fact, the only postulate made about the system is that a balance relation exists among the system variables, involving the measured quantities (e.g. inputs and outputs) and the state of the system.