Artificial neural networks in modulating complex dynamics: Theory and ApplicationAbstract: Dynamical systems are pervasive in nature and engineering, appearing in areas such as neuroscience, life sciences, and molecular dynamics. However, due to nonlinear interactions, network structures, stochastic perturbations, and time delays, these systems often exhibit highly intricate behaviours that are difficult to control or stabilize. This work integrates control and stability theories with neural network architectures to modulate the evolution of complex dynamical systems. Specifically, it develops theoretical frameworks and algorithms for regulating steady states and synchronizing stochastic and delayed networked systems. The study addresses three key challenges in applying neural networks to dynamical systems: the lack of theoretical guarantees, high computational cost, and difficulty in controlling underactuated systems. The proposed methods achieve improved convergence, energy efficiency, and robustness compared to existing state-of-the-art approaches. Finally, the framework is extended to generative modelling, demonstrating its potential application for controlling high-dimensional dynamical processes. |