Neural network augmented modeling with applications to active matterTitus QuahModel Predictive Control (MPC) is an effective algorithm that has been widely successful in various fields such as chemical processing and manufacturing. However, MPC is reliant on an accurate dynamic model to constrain the state dynamics in the optimal control problem. In practice, obtaining a high fidelity dynamical model is difficult and as the system changes over time, the model prediction accuracy worsens. Thus, we propose a data-driven method that combines MPC with Neural Network Augmented Models (NNAMs). NNAMs take partially known dynamics obtained from domain knowl- edge, e.g., mass or momentum balances, and approximate the unknown terms that are difficult to model with Neural Network (NNs). The NN parameters are estimated by solving a multi- step ahead prediction error minimization problem. This model is then used in MPC to control the system of interest. Our objective is to apply this method to control a partial differential equations describing dynamics of active matter systems. |