Title:  Deep Learning for Dynamical Systems: Learning to Model, Predict and Control

Committee: 

Dr. Mukhopadhyay, Advisor    

Dr. Chatterjee, Chair

Dr. Romberg

Abstract: The objective of the proposed research is to develop deep learning methods for data-driven prediction and control of dynamical systems. One branch of this research focuses on the prediction problem as an independent task and investigates deep neural network (DNN) models for two different types of dynamical systems: (1) multi-agent interaction dynamics and (2) spatiotemporal physical processes.  To predict the time evolution of multi-agent dynamical systems, a DNN-based multi-agent interaction model is developed, which can adapt to the changes in physical or relational attributes of the agents, or changes in the number of agents from online observation. For spatiotemporal physical processes, both pure data-driven and physics-informed hybrid deep models are studied. A physics-incorporated recurrent model is introduced for source identification and forecasting of spatiotemporal dynamical systems with unobservable time-varying external sources.  For pure data-driven modeling of spatiotemporal physical processes, a deep learning framework is developed that can learn prediction models using data collected from sparse and irregularly distributed data sites. The other branch of the proposed research focuses on learning control policies for nonlinear dynamical systems using DNNs. A novel method for nonlinear control design coupling deep learning with control theory is introduced. The remainder of the study will focus on developing data-driven control for spatiotemporal dynamical systems by combining the designed frameworks from the aforementioned branches of prediction and control.