Constructing Neural Network Based Models for Simulating Dynamical Systems

Christian Møldrup Legaard, Thomas Schranz, Gerald Schweiger, Jan Drgona, Basak Falay, Cláudio Gomes, Alexandros Iosifidis, Mahdi Abkar, Peter Gorm Larsen

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


Dynamical systems see widespread use in natural sciences like physics, biology, and 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 applying data-driven modeling techniques to solve a wide range of problems in physics and engineering. This article 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.

Original languageEnglish
Article number236
JournalACM Computing Surveys
Pages (from-to)1-34
Number of pages34
Publication statusPublished - Feb 2023


  • Additional Key Words and PhrasesNeural ODEs
  • physics-based regularization
  • physics-informed neural networks


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