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

The development of stable, accurate, and generalizable numerical simulation methods remains a critical challenge in computational fluid dynamics (CFD). Recently, physics-informed neural networks (PINNs) have emerged as a promising approach by embedding physical laws directly into the loss function of neural networks, enabling mesh-free solutions of governing equations. PINNs offer a new perspective on CFD and open a significant pathway for AI for science. However, existing PINN models often face trade-offs between generality, stability, and accuracy. To address these trade-offs, this paper proposes a novel hybrid architecture, PINN-MRT, which integrates the multi-relaxation-time lattice Boltzmann method (MRT-LBM) with PINNs. For the first time, the MRT-LBM evolution equation is embedded as the physics-informed residual within the loss function. Due to the mesoscopic kinetic nature of the MRT-LBM equations, the proposed PINN-MRT inherently possesses the potential for fluid solution generality. The PINN-MRT adopts a dual-network architecture, which separately predicts macroscopic conserved variables and non-equilibrium distribution functions. A composite loss function is then constructed to incorporate physical residuals, boundary conditions, and data-driven terms, enabling the PINN-MRT architecture to simultaneously address both forward and inverse problems. Numerical validation on both forward and inverse problems confirms the superior stability and predictive accuracy of the proposed PINN-MRT model, demonstrating significant improvements over the standard PINN and existing PINN-LBM hybrid architectures. This study provides a novel stable, accurate, and generalizable PINN architecture for CFD research.