A Survey on Neural Dynamics for Computing and Control: Theories, Models, and Applications

Long Jin

Abstract

Neural dynamics provides a powerful and unifying tool for understanding systems that learn, adapt, and interact. This survey provides a comprehensive overview of the theories, models, and applications of neural dynamics at the intersection of computing and control. We first articulate the core concept of neural dynamics, explaining the close connection between this concept and dynamical system theory. We then demonstrate the broad applicability of neural dynamics by reviewing a wide range of models across various key domains. In the field of control, we survey neural dynamics approaches to classical problems of stability and optimality, especially within control systems and multi-agent systems (MASs). In the field of computing, we focus on deep learning, analyzing both model architectures and optimizers as different dynamical systems. The principal contribution of this work is to bridge these domains, revealing the computation and control topics governed by neural dynamics theories. This integrated viewpoint illuminates numerous applications and inspires future research directions focusing on advanced models in terms of computation and control.

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