Controlling synchronization dynamics via physics-informed neural networks

Area of Science:

• Complex Systems
• Control Theory
• Artificial Intelligence

Background:

• Networked dynamical systems require precise control over synchronization, encompassing timing and coherence levels.
• Existing methods often lack the flexibility to simultaneously regulate these synchronization characteristics.

Purpose of the Study:

• To introduce a novel physics-informed neural network (PINN) framework for continuous-time synchronization regulation.
• To enable simultaneous control of synchronization time and coherence level without explicit feedback or optimal control problem solutions.

Main Methods:

• Joint parameterization of system trajectories and control inputs, constrained by governing dynamics.
• Imposition of macroscopic synchronization objectives via persistence conditions on the order parameter at target times.
• Application of the framework to networked Kuramoto oscillators.

Main Results:

• Demonstrated smooth synchronization with reduced transient control effort compared to analytical baselines.
• Achieved competitive cumulative cost relative to analytical methods.
• Framework effectiveness shown in nongradient and frustrated dynamics, including chimera and chaotic states.

Conclusions:

• Physics-informed neural control offers a flexible, trajectory-level approach for synchronization regulation in complex systems.
• The framework provides controlled access to nontrivial collective states, advancing the understanding and manipulation of networked dynamics.