Reinforcement Learning for Self-adapting Time Discretizations of Complex Systems

The overarching goal of this project is to develop intelligent, self-adapting numerical algorithms for the time discretization of complex real-world problems with Q-Learning methodologies. The specific application is ordinary differential equations which can resolve problems in mathematics, social and natural sciences, but which usually require approximations to solve because direct analytical solutions are rare. Using the traditional Brusellator and Lorenz differential equations as test beds, this research develops models to determine reward functions and dynamically tunes controller parameters that minimize both the error and number of steps required for approximate mathematical solutions. Our best reward function is based on an error that does not overly punish rejected states. The Alpha-Beta Adjustment and Safety Factor Adjustment Model is the most efficient and accurate method for solving these mathematical problems. Allowing the model to change the alpha/beta value and safety factor by small amounts provides better results than if the model chose values from discrete lists. This method shows potential for training dynamic controllers with Reinforcement Learning.