Deep reinforcement learning for adaptive mesh refinement

Corbin Foucart

doi:10.1016/j.jcp.2023.112381

Deep reinforcement learning for adaptive mesh refinement

2023-10-01

10

OA

AI

Pierre F. J. Lermusiaux *

DOI：10.1016/j.jcp.2023.112381

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Abstract

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Finite element discretizations of problems in computational physics often rely on adap-tive mesh refinement (AMR) to preferentially resolve regions containing important features during simulation. However, these spatial refinement strategies are often heuristic and rely on domain-specific knowledge or trial-and-error. We treat the process of adaptive mesh refinement as a local, sequential decision-making problem under incomplete information, formulating AMR as a partially observable Markov decision process. Using a deep rein-forcement learning (RL) approach, we train policy networks for AMR strategy directly from numerical simulation. The training process does not require an exact solution or a high-fidelity ground truth to the partial differential equation (PDE) at hand, nor does it require a pre-computed training dataset. The local nature of our deep RL (DRL) allows the pol-icy network to be trained inexpensively on much smaller problems than those on which they are deployed. The new DRL-AMR method is not specific to any particular PDE, prob-lem dimension, or numerical discretization. The RL policy networks, trained on simple examples, can generalize to more complex problems, and can flexibly incorporate diverse problem physics. To that end, we apply the method to a range of PDEs, using a variety of high-order discontinuous Galerkin and hybridizable discontinuous Galerkin finite element discretizations. We show that the resultant DRL policies are competitive with common AMR heuristics and strike a favorable balance between accuracy and cost such that they often lead to a higher accuracy per problem degree of freedom, and are effective across a wide class of PDEs and problems.(c) 2023 Elsevier Inc. All rights reserved.

Keywords:

Reinforcement learning

Adaptive mesh refinement

Finite element methods

Computational fluid dynamics

Ocean modeling

Atmospheric forecasting

Deep reinforcement learning for adaptive mesh refinement

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