Improved physics-informed neural networks incorporating lattice Boltzmann method optimized by tanh robust weight initialization

Abstract Physics-informed neural networks (PINNs) have shown considerable promise for performing numerical simulations in fluid mechanics. They provide mesh-free, end-to-end approaches by embedding physical laws into their loss functions. However, when addressing complex flow problems, PINNs still face some challenges such as activation saturation and vanishing gradients in deep network training, leading to slow convergence and insufficient prediction accuracy. We present physics-informed neural networks incorporating lattice Boltzmann method optimized by tanh robust weight initialization (T-PINN-LBM) to address these challenges. This approach fuses the mesoscopic lattice Boltzmann model with the automatic differentiation framework of PINNs. It also implements a tanh robust weight initialization method derived from fixed point analysis. This model effectively mitigates activation and gradient decay in deep networks, improving convergence speed and data efficiency in multiscale flow simulations. We validate the effectiveness of the model on the classical arithmetic example of lid-driven cavity flow. Compared to the traditional Xavier initialized PINN and PINN-LBM, T-PINN-LBM reduces the mean absolute error (MAE) by one order of magnitude at the same network depth and maintains stable convergence in deeper networks. The results demonstrate that this model can accurately capture complex flow structures without prior data, providing a new feasible pathway for data-free driven fluid simulation.