Towards Reinforcement Learning Driven Mesh Adaptivity for Second Order Elliptic Problems
Abstract
Adaptive mesh refinement techniques have become an indispensable tool in achieving accurate and efficiently computed solutions to problems which require impractically fine uniform meshes to obtain an accurate approximation. The adaptive algorithm involves a recursive application of SOLVE-ESTIMATE-MARK-REFINE steps where in particular the step `ESTIMATE' involves computing a posteriori error estimator based on only the numerical solution and the data of the problem. Over the years, several a posteriori error estimators have been developed and successfully applied but often times, the choice of estimator is ill suited for the problem at hand. In this research, we present two estimators namely the residual-based estimator and the gradient recovery type estimator and illustrate the suitability of these estimators for different problems at hand. We also provide the foundation for data-driven adaptive mesh refinement strategies based on Reinforcement learning (RL) with a focus on the Q-learning algorithm which is a fundamental learning algorithm in RL.
Subject Area
Mathematics|Computer science|Applied Mathematics
Recommended Citation
Twumasi, Augustine, "Towards Reinforcement Learning Driven Mesh Adaptivity for Second Order Elliptic Problems" (2021). ETD Collection for University of Texas, El Paso. AAI28715096.
https://scholarworks.utep.edu/dissertations/AAI28715096