2023/04/03 by Niklas Freymuth, Philipp Dahlinger, Freymuth, Niklas +8 · 3 citations
Computer Science · Decision Sciences · Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Manufacturing Process and Optimization #Model-Driven Software Engineering Techniques #Multiagent Systems (cs.MA) #Numerical Analysis (math.NA) #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2304.00818
openalex publication_date 2023/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Adaptive Mesh Refinement (AMR) enhances the Finite Element Method, an important technique for simulating complex problems in engineering, by dynamically refining mesh regions, enabling a favorable trade-off between computational speed and simulation accuracy. Classical methods for AMR depend on heuristics or expensive error estimators, hindering their use for complex simulations. Recent learning-based AMR methods tackle these issues, but so far scale only to simple toy examples. We formulate AMR as a novel Adaptive Swarm Markov Decision Process in which a mesh is modeled as a system of simple collaborating agents that may split into multiple new agents. This framework allows for a spatial reward formulation that simplifies the credit assignment problem, which we combine with Message Passing Networks to propagate information between neighboring mesh elements. We experimentally validate our approach, Adaptive Swarm Mesh Refinement (ASMR), on challenging refinement tasks. Our approach learns reliable and efficient refinement strategies that can robustly generalize to different domains during inference. Additionally, it achieves a speedup of up to 2 orders of magnitude compared to uniform refinements in more demanding simulations. We outperform learned baselines and heuristics, achieving a refinement quality that is on par with costly error-based oracle AMR strategies.