构造基于神经网络的动态系统仿真模型
Constructing Neural Network-Based Models for Simulating Dynamical Systems
摘要：
动力学系统广泛应用于物理学、生物学、化学等自然科学以及电路分析、计算流体动力学和控制等工程学科。对于简单的系统，控制动力学的微分方程可以通过应用基本物理定律导出。然而，对于更复杂的系统，这种方法变得非常困难。数据驱动建模是一种替代范式，它试图通过对真实系统的观察来学习系统动态的近似值。近年来，人们对数据驱动的建模技术越来越感兴趣，特别是神经网络已被证明为解决各种任务提供了有效的框架。本文综述了用神经网络建立动态系统模型的不同方法。除了基本的概述，我们回顾了相关的文献，并概述了最重要的挑战，从数值模拟，这种建模范式必须克服。基于回顾的文献和确定的挑战，我们提供了一个有前途的研究领域的讨论。
英文摘要：
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential equations governing the dynamics can be derived by applying fundamental physical laws. However, for more complex systems, this approach becomes exceedingly difficult. Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. In recent years, there has been an increased interest in data-driven modeling techniques, in particular neural networks have proven to provide an effective framework for solving a wide range of tasks. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome. Based on the reviewed literature and identified challenges, we provide a discussion on promising research areas.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
