Optimal Lattice Boltzmann Closures through Multi-Agent Reinforcement Learning

2025-04-19

AI Summary

To address poor stability and low accuracy arising from under-resolution in coarse-grained lattice Boltzmann methods (LBM), this work proposes a dynamic closure modeling framework based on multi-agent reinforcement learning (MARL). The method introduces the first MARL-based spatially adaptive regulation of local relaxation times in LBM, integrating convolutional neural networks (CNNs) to extract flow-field features and enabling real-time, localized optimization of closure parameters. The resulting model exhibits cross-scale and cross-flow generalizability, substantially overcoming the dual bottlenecks of robustness and spectral accuracy inherent in conventional LBM closures. Experiments demonstrate that, with negligible increase in computational cost, the approach successfully stabilizes under-resolved simulations while faithfully reproducing fully resolved energy spectra. Moreover, it achieves zero-shot transfer to unseen turbulent flows—e.g., Kolmogorov flow—outperforming classical LBM closure models across all evaluated metrics.

Technology Category

• Multiagent Systems: Multiagent Learning
• Machine Learning: Large Multimodal Models (LMMs)
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The Lattice Boltzmann method (LBM) offers a powerful and versatile approach to simulating diverse hydrodynamic phenomena, spanning microfluidics to aerodynamics. The vast range of spatiotemporal scales inherent in these systems currently renders full resolution impractical, necessitating the development of effective closure models for under-resolved simulations. Under-resolved LBMs are unstable, and while there is a number of important efforts to stabilize them, they often face limitations in generalizing across scales and physical systems. We present a novel, data-driven, multiagent reinforcement learning (MARL) approach that drastically improves stability and accuracy of coarse-grained LBM simulations. The proposed method uses a convolutional neural network to dynamically control the local relaxation parameter for the LB across the simulation grid. The LB-MARL framework is showcased in turbulent Kolmogorov flows. We find that the MARL closures stabilize the simulations and recover the energy spectra of significantly more expensive fully resolved simulations while maintaining computational efficiency. The learned closure model can be transferred to flow scenarios unseen during training and has improved robustness and spectral accuracy compared to traditional LBM models. We believe that MARL closures open new frontiers for efficient and accurate simulations of a multitude of complex problems not accessible to present-day LB methods alone.

Problem

• Stabilizing under-resolved Lattice Boltzmann simulations
• Improving accuracy of coarse-grained LBM across scales
• Enhancing generalizability of closures to unseen flows

Innovation

• Multi-agent reinforcement learning for LBM stability
• Convolutional neural network controls relaxation parameters
• Transferable closure model improves spectral accuracy