Physics informed neural networks for fluid flow analysis with repetitive parameter initialization

Physics-informed neural networks (PINNs) have been widely used to capture the behavior of physical systems governed by partial differential equations (PDEs), enabling the simulation of fluid dynamics across various scenarios. However, when applied to stiff fluid problems, the existing PINNs often struggle with flow stagnations and converge to local minima, resulting in physically implausible solutions. To overcome these limitations, this study proposes a training strategy called "re-initialization". This strategy periodically modulates the training parameters of the PINN model, enabling it to escape local minima and effectively explore alternative solutions. The proposed method is validated on two-dimensional steady-state lid-driven cavity flow problems at high Reynolds numbers of 700 and 1,000. This strategy effectively simulated vortex and shear layers and achieved the lowest mean square error in both cases. Furthermore, principal component analysis confirmed its capability to dynamically modulate model parameters during the training process. These results show the effectiveness of the proposed training strategy in addressing stiff fluid problems. Moreover, this strategy establishes a foundation for overcoming local minima through the direct modulation of training parameters. This contribution not only enhances the accuracy of PINNs but also expands their applicability to more complex and stiff fluid flow analyses.