Publication Date

12-2025

Date of Final Oral Examination (Defense)

9-25-2025

Type of Culminating Activity

Thesis

Degree Title

Master of Science in Mathematics

Department

Mathematics

Supervisory Committee Chair

Michal Kopera, Ph.D.

Supervisory Committee Member

Donna Calhoun, Ph.D.

Supervisory Committee Member

Grady Wright, Ph.D.

Abstract

Adaptive mesh refinement (AMR) enables efficient solution of partial differential equations by dynamically allocating computational resources to regions requiring higher resolution. It has been demonstrated that deep reinforcement learning agents could learn effective mesh adaptation policies. However, practical deployment requires a systematic understanding of how training parameters affect performance across diverse computational scenarios.

This thesis presents a parameter optimization study analyzing the relationship between deep reinforcement learning for adaptive mesh refinement (DRL-AMR) training parameters and model performance. We implement an independent DRL-AMR system with a discontinuous Galerkin solver and actor-critic (A2C) algorithm for one-dimensional linear advection. The study explores four key parameters across 81 training configurations, with each model evaluated across nine deployment scenarios for 729 total assessments.

Using Pareto optimization techniques, we identify optimal parameter combinations for different deployment objectives. Results show that properly configured DRL-AMR models achieve 80\% to 88\% computational cost savings compared to full-refinement no-AMR baselines while maintaining comparable accuracy to traditional AMR methods.

This work contributes a systematic parameter sensitivity analysis and multi-objective optimization framework providing a foundation for advancing DRL-AMR research toward practical computational tools for scientific computing applications.

DOI

https://doi.org/10.18122/td.2447.boisestate

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