基于（端口哈密顿）微分代数方程的数学建模、仿真与优化

中文摘要 AI 辅助

微分代数方程（DAEs）在复杂有限维或无限维动态系统的自动化建模、仿真、控制和优化中构成了一类普遍存在的模型类，特别是在数字孪生的构建中。当与适当的空间和时间离散化方法相结合时，它们成为许多工程领域发展的主力工具。然而，这种方法给数值方法带来了某些挑战，尤其是在耦合来自不同物理领域、具有不同尺度或正则性要求的系统时。我们综述了基于DAEs的建模，并探讨如何通过端口哈密顿微分代数系统（pHDAEs）框架及其结合时空模型自适应方法的仿真与优化来克服部分挑战。

英文摘要

Differential-algebraic equations (DAEs) present a ubiquitous model class in the automated modeling, simulation, control and optimization of complex finite or infinite dimensional dynamical systems, in particular in the construction of digital twins. When combined with adequate space and time discretization methods they present the work-horse of developments in many engineering domains. However, this approach comes with certain challenges for the numerical methods and in particular in the coupling of systems from different physical domains with different scales or regularity requirements. We survey the modeling with DAEs and address how to overcome some of the challenges via the framework of port-Hamiltonian differential-algebraic systems (pHDAEs) and their simulation and optimization with space-time-model adaptive methods.

发表机构

• TU Berlin（柏林工业大学）

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