  In this paper we propose a new computational method for designing optimal
regulators for high-dimensional nonlinear systems. The proposed approach
leverages physics-informed machine learning to solve high-dimensional
Hamilton-Jacobi-Bellman equations arising in optimal feedback control.
Concretely, we augment linear quadratic regulators with neural networks to
handle nonlinearities. We train the augmented models on data generated without
discretizing the state space, enabling application to high-dimensional
problems. We use the proposed method to design a candidate optimal regulator
for an unstable Burgers' equation, and through this example, demonstrate
improved robustness and accuracy compared to existing neural network
formulations.
