PROJECT SUMMARY A standing challenge in neuroscience is to control the activity of large populations of interconnected neurons that underlie our brain’s functions and dysfunctions. The dynamics of these neural activity patterns are immensely complex and nonlinear, making their modeling extremely difficult. Thus, the precise control of neural dynamics and the associated mental states using stimulation input has remained elusive to date. If precise dynamic modeling and control was possible, this would both elucidate the neural basis of behavior and treat the most prevalent and disabling mental disorders such as depression or addiction, which are a leading cause of disability worldwide. The goal of this innovative proposal is to move toward making this vision a reality. We will: (1) develop a novel biologically-informed geometric paradigm to achieve nonlinear dynamic modeling and closed-loop control of neural population activity; (2) demonstrate it on brain network activity collected from the monkey motor system and the human corticolimbic system to characterize the neural dynamics of complex movements and control the neural biomarkers of depressed mood, respectively. This geometric paradigm will be based on a central idea: if we learn and model the low-dimensional nonlinear geometric space over which neural population activity evolves in time, we can then analytically write the dynamic model in a much simpler form over this manifold; this will allow for precise modeling of nonlinear dynamics and enable their control, which is otherwise impractical. Capturing the nonlinearity in the geometry to achieve control of brain dynamics with unprecedented precision is a major innovation and departure from current methods. We introduce concepts from algebraic topology and differential geometry into neural dynamic modeling and control. We will develop new methods at the interface of these disciplines, neuroscience, machine learning and control theory to: (1) identify the type of manifold that embeds neural dynamics (e.g., torus or sphere); (2) develop novel algorithms that learn analytical dynamic models over this manifold (both with and without stimulation input); (3) build decoders and controllers of neural dynamics that incorporate the biologically-informed nonlinear geometric models. We will provide three rigorous experimental demonstrations on rich data from two distinct neural systems: (i) existing spike-field activity from monkey motor cortices during complex reach-and-grasps; (ii) existing multisite intracranial human brain activity in the corticolimbic system with simultaneous mood tracking; (iii) new closed-loop control experiments to selectively modulate brain network activity underlying mood states in the corticolimbic system using electrical stimulation. The paradigm will provide a new tool to build interpretable, low-dimensional, and controllable nonlinear models of neural dynamics to elucidate the neural basis of behavior and disease. Also, it w...