Solving control problems with physics informed machine learning for partial differential equations

Physics informed machine learning consists of various machine learning methods for learning partial differential equation (PDE) models and solutions. We empirically study three methods from this field for learning solutions to a PDE model, focusing on the Hamilton Jacobi Bellman PDE for continuous time control. We find that the methods learn accurate solutions for high dimensional linear systems. Although the methods have some shortcomings, they achieve promising results on the Cartpole task from nonlinear control.

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