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Constructing Neural Network-Based Models for Simulating Dynamical Systems

arXiv 2111.01495 ↗First posted 2 Nov 2021cs.LGcited by 31

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Abstract (arXiv)

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.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). Builds on 78 of its 141 references that are in the map. First posted on arXiv 2 Nov 2021.

Builds on

78 of 141 references.

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50 most cited of 78 All 78 (JSON)

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Citing papers per year: 2022: 4; 2023: 4; 2024: 9; 2025: 10; 2026: 4.

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  10. 2025Meta-Learning for Physically-Constrained Neural System Identificationcited by 6
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  6. 2024Domain-specific ReAct for physics-integrated iterative modeling: A case study of LLM agents for gas path analysis of gas turbinescited by 1
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  8. 2025A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Seriescited by 1
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  17. 2026Safe-by-Design Learning via Energy-based Neural Networkscited by 0
  18. 2026Variational Augmented Invertible Koopman Autoencoder for probabilistic time series forecastingcited by 0
  19. 2026Dirac-Interconnected Neural Elements: Discovering Modularity in Physical Systems Without Reductioncited by 0