Adaptive Swarm Mesh Refinement using Deep Reinforcement Learning with Local Rewards

• URL: http://arxiv.org/abs/2406.08440v1
• Date: Wed, 12 Jun 2024 17:26:54 GMT
• Title: Adaptive Swarm Mesh Refinement using Deep Reinforcement Learning with Local Rewards
• Authors: Niklas Freymuth, Philipp Dahlinger, Tobias Würth, Simon Reisch, Luise Kärger, Gerhard Neumann,
• Abstract summary: Adaptive Mesh Refinement (AMR) improves the Finite Element Method (FEM) We formulate AMR as a system of collaborating, homogeneous agents that iteratively split into multiple new agents. Our approach, Adaptive Swarm Mesh Refinement (ASMR), offers efficient, stable optimization and generates highly adaptive meshes at user-defined resolution during inference.
• Score: 12.455977048107671
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simulating physical systems is essential in engineering, but analytical solutions are limited to straightforward problems. Consequently, numerical methods like the Finite Element Method (FEM) are widely used. However, the FEM becomes computationally expensive as problem complexity and accuracy demands increase. Adaptive Mesh Refinement (AMR) improves the FEM by dynamically allocating mesh elements on the domain, balancing computational speed and accuracy. Classical AMR depends on heuristics or expensive error estimators, limiting its use in complex simulations. While learning-based AMR methods are promising, they currently only scale to simple problems. In this work, we formulate AMR as a system of collaborating, homogeneous agents that iteratively split into multiple new agents. This agent-wise perspective enables a spatial reward formulation focused on reducing the maximum mesh element error. Our approach, Adaptive Swarm Mesh Refinement (ASMR), offers efficient, stable optimization and generates highly adaptive meshes at user-defined resolution during inference. Extensive experiments, including volumetric meshes and Neumann boundary conditions, demonstrate that ASMR exceeds heuristic approaches and learned baselines, matching the performance of expensive error-based oracle AMR strategies. ASMR additionally generalizes to different domains during inference, and produces meshes that simulate up to 2 orders of magnitude faster than uniform refinements in more demanding settings.

Related papers

• Federated Conditional Stochastic Optimization [110.513884892319]
  Conditional optimization has found in a wide range of machine learning tasks, such as in-variant learning tasks, AUPRC, andAML. This paper proposes algorithms for distributed federated learning.
  arXiv  Detail & Related papers  (2023-10-04T01:47:37Z)
• Swarm Reinforcement Learning For Adaptive Mesh Refinement [11.201100158465394]
  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.
  arXiv  Detail & Related papers  (2023-04-03T09:07:17Z)
• Multi-Agent Reinforcement Learning for Adaptive Mesh Refinement [17.72127385405445]
  We present a novel formulation of adaptive mesh refinement (AMR) as a fully-cooperative Markov game. We design a novel deep multi-agent reinforcement learning algorithm called Value Decomposition Graph Network (VDGN) We show that VDGN policies significantly outperform error threshold-based policies in global error and cost metrics.
  arXiv  Detail & Related papers  (2022-11-02T00:41:32Z)
• Deep Reinforcement Learning for Adaptive Mesh Refinement [0.9281671380673306]
  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. We show that the deep reinforcement learning policies are competitive with common AMRs, generalize well across problem classes, and strike a favorable balance between accuracy and cost.
  arXiv  Detail & Related papers  (2022-09-25T23:45:34Z)
• Collaborative Intelligent Reflecting Surface Networks with Multi-Agent Reinforcement Learning [63.83425382922157]
  Intelligent reflecting surface (IRS) is envisioned to be widely applied in future wireless networks. In this paper, we investigate a multi-user communication system assisted by cooperative IRS devices with the capability of energy harvesting.
  arXiv  Detail & Related papers  (2022-03-26T20:37:14Z)
• Efficient Model-Based Multi-Agent Mean-Field Reinforcement Learning [89.31889875864599]
  We propose an efficient model-based reinforcement learning algorithm for learning in multi-agent systems. Our main theoretical contributions are the first general regret bounds for model-based reinforcement learning for MFC. We provide a practical parametrization of the core optimization problem.
  arXiv  Detail & Related papers  (2021-07-08T18:01:02Z)
• Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimization [85.84019017587477]
  Distributionally robust supervised learning is emerging as a key paradigm for building reliable machine learning systems for real-world applications. Existing algorithms for solving Wasserstein DRSL involve solving complex subproblems or fail to make use of gradients. We revisit Wasserstein DRSL through the lens of min-max optimization and derive scalable and efficiently implementable extra-gradient algorithms.
  arXiv  Detail & Related papers  (2021-04-27T16:56:09Z)
• Reinforcement Learning for Adaptive Mesh Refinement [63.7867809197671]
  We propose a novel formulation of AMR as a Markov decision process and apply deep reinforcement learning to train refinement policies directly from simulation. The model sizes of these policy architectures are independent of the mesh size and hence scale to arbitrarily large and complex simulations.
  arXiv  Detail & Related papers  (2021-03-01T22:55:48Z)
• Multiple-shooting adjoint method for whole-brain dynamic causal modeling [8.943170877509923]
  Multiple-Shooting Adjoint (MSA) is suitable for large-scale systems such as whole-brain analysis in functional MRI (fMRI) MSA achieves better accuracy in parameter value estimation than EM. We show improved classification of autism spectrum disorder (ASD) vs. control compared to using the functional connectome.
  arXiv  Detail & Related papers  (2021-02-14T05:00:12Z)
• Modal Regression based Structured Low-rank Matrix Recovery for Multi-view Learning [70.57193072829288]
  Low-rank Multi-view Subspace Learning has shown great potential in cross-view classification in recent years. Existing LMvSL based methods are incapable of well handling view discrepancy and discriminancy simultaneously. We propose Structured Low-rank Matrix Recovery (SLMR), a unique method of effectively removing view discrepancy and improving discriminancy.
  arXiv  Detail & Related papers  (2020-03-22T03:57:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.