Swarm Reinforcement Learning For Adaptive Mesh Refinement
- URL: http://arxiv.org/abs/2304.00818v2
- Date: Fri, 28 Jul 2023 14:02:32 GMT
- Title: Swarm Reinforcement Learning For Adaptive Mesh Refinement
- Authors: Niklas Freymuth, Philipp Dahlinger, Tobias W\"urth, Simon Reisch,
Luise K\"arger, Gerhard Neumann
- Abstract summary: We develop a novel AMR that learns reliable, scalable, and efficient refinement strategies on a set of challenging problems.
Our approach significantly speeds up, achieving up to 30-fold improvement compared to uniform refinements in complex simulations.
- Score: 11.201100158465394
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The Finite Element Method, an important technique in engineering, is aided by
Adaptive Mesh Refinement (AMR), which dynamically refines mesh regions to allow
for a favorable trade-off between computational speed and simulation accuracy.
Classical methods for AMR depend on task-specific heuristics or expensive error
estimators, hindering their use for complex simulations. Recent learned AMR
methods tackle these problems, 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 the effectiveness of our approach, Adaptive Swarm Mesh
Refinement (ASMR), showing that it learns reliable, scalable, and efficient
refinement strategies on a set of challenging problems. Our approach
significantly speeds up computation, achieving up to 30-fold improvement
compared to uniform refinements in complex simulations. Additionally, we
outperform learned baselines and achieve a refinement quality that is on par
with a traditional error-based AMR strategy without expensive oracle
information about the error signal.
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