Hybrid Physics-Informed Neural Networks Integrating Multi-Relaxation-Time Lattice Boltzmann Method for Forward and Inverse Flow Problems

Mengyu Feng, Minglei Shan (), Ling Kuai, Chenghui Yang, Yu Yang, Cheng Yin and Qingbang Han
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Mengyu Feng: College of Information Science and Engineering, Hohai University, Changzhou 213200, China
Minglei Shan: College of Information Science and Engineering, Hohai University, Changzhou 213200, China
Ling Kuai: College of Information Science and Engineering, Hohai University, Changzhou 213200, China
Chenghui Yang: College of Information Science and Engineering, Hohai University, Changzhou 213200, China
Yu Yang: College of Information Science and Technology, Nanjing Forestry University, Nanjing 210037, China
Cheng Yin: College of Information Science and Engineering, Hohai University, Changzhou 213200, China
Qingbang Han: College of Information Science and Engineering, Hohai University, Changzhou 213200, China

Mathematics, 2025, vol. 13, issue 22, 1-22

Abstract: Although physics-informed neural networks (PINNs) offer a novel, mesh-free paradigm for computational fluid dynamics (CFD), existing models often suffer from poor stability and insufficient accuracy, particularly when dealing with complex flows at high Reynolds numbers. To address this limitation, we propose, for the first time, a novel hybrid architecture, PINN-MRT, which integrates the multi-relaxation-time lattice Boltzmann method (MRT-LBM) with PINNs. The model embeds the MRT-LBM evolution equation as a physical constraint within the loss function and employs a unique dual-network architecture to separately predict macroscopic conserved variables and non-equilibrium distribution functions, enabling both forward and inverse problem-solving through a composite loss function. Benchmark tests on the lid-driven cavity flow demonstrate the superior performance of PINN-MRT. In inverse problems, it remains stable at Reynolds numbers up to 5000 with parameter inversion errors below 15%, whereas standard PINN and single-relaxation-time PINN-LBM models fail at a Reynolds number of 1000 with errors exceeding 80%. In purely physics-driven forward problems, PINN-MRT also provides stable solutions at a Reynolds number of 400, while the other models completely collapse. This study confirms that incorporating mesoscopic kinetic theory into PINNs effectively overcomes the stability bottlenecks of conventional approaches, providing a more robust and accurate architecture for CFD and paving the way for solving more challenging fluid dynamics problems.

Keywords: physics-informed neural networks; multi-relaxation-time lattice Boltzmann method; computational fluid dynamics; deep learning (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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