Firing pattern manipulation of neuronal networks by deep unfolding-based model predictive control

The complexity of neuronal networks, characterized by interconnected neurons, presents significant challenges in control due to their nonlinear and intricate behaviour. This paper introduces a novel method designed to generate control inputs for neuronal networks to regulate the firing patterns of modules within the network. This methodology is built upon temporal deep unfolding-based model predictive control, a technique rooted in the deep unfolding method commonly used in wireless signal processing. To address the unique dynamics of neurons, such as zero gradients in firing times, the method employs approximations of input currents using a sigmoid function during its development. The effectiveness of this approach is validated through extensive numerical simulations. Furthermore, control experiments were conducted by reducing the number of input neurons to identify critical features for control. Various selection techniques were utilized to pinpoint key input neurons. These experiments shed light on the importance of specific input neurons in controlling module firing within neuronal networks. Thus, this study presents a tailored methodology for managing networked neurons, extends temporal deep unfolding-based model predictive control to nonlinear systems with reset dynamics, and demonstrates its ability to achieve desired firing patterns in neuronal networks.