Reinforcement Learning-Based Model Reduction for Partial Differential Equations: Application to the Burgers Equation

Partial differential equations (PDEs) are important mathematical models, which are used to model complex dynamic systems in applied sciences. For example, PDEs are used to model flexible beams and ropes [1, 2], crowd dynamics [3, 4], or fluid dynamics [5, 6]. However, PDEs are infinite-dimensional systems, making them hard to solve in closed form, and computationally demanding to solve numerically. For instance, when using finite element methods (FEM), one may end up with a very large discretization space, which incurs large computation times. Because of this complexity, it is often hard to use PDEs to analyze, predict, or control these systems in real time.