Reinforcement learning for anisotropic p-adaptation and error estimation in high-order solvers

TL;DR

This paper introduces a reinforcement learning-based method to automate and optimize anisotropic p-adaptation in high-order solvers, improving accuracy and efficiency in complex 3D fluid simulations.

Contribution

It develops a novel RL-driven approach for dynamic mesh adaptation and error estimation, applicable to various PDEs and mesh types, with minimal computational overhead.

Findings

Effective RL-based error estimation quantifies local discretization errors.

Automated anisotropic p-adaptation reduces manual intervention and computational costs.

Validated on laminar and turbulent flow cases, demonstrating flexibility and robustness.

Abstract

We present a novel approach to automate and optimize anisotropic p-adaptation in high-order h/p solvers using Reinforcement Learning (RL). The dynamic RL adaptation uses the evolving solution to adjust the high-order polynomials. We develop an offline training approach, decoupled from the main solver, which shows minimal overcost when performing simulations. In addition, we derive an inexpensive RL-based error estimation approach that enables the quantification of local discretization errors. The proposed methodology is agnostic to both the computational mesh and the partial differential equation to be solved. The application of RL to mesh adaptation offers several benefits. It enables automated and adaptive mesh refinement, reducing the need for manual intervention. It optimizes computational resources by dynamically allocating high-order polynomials where necessary and minimizing refinement in stable regions. This leads to computational cost savings while maintaining the accuracy of the solution. Furthermore, RL allows for the exploration of unconventional mesh adaptations, potentially enhancing the accuracy and robustness of simulations. This work extends our original research, offering a more robust, reproducible, and generalizable approach applicable to complex three-dimensional problems. We provide validation for laminar and turbulent cases: circular cylinders, Taylor Green Vortex and a 10MW wind turbine to illustrate the flexibility of the proposed approach.