Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs) by directly embedding them into the loss function. Despite their notable success, existing PINNs often exhibit training instability and slow convergence when applied to strongly nonlinear fluid dynamics problems. To address these challenges, this paper proposes a novel PINN framework, named as SIMPLE-PINN, which incorporates velocity and pressure correction loss terms inspired by the semi-implicit pressure link equation. These correction terms, derived from the momentum and continuity residuals, are tailored for the PINN framework, ensuring velocity-pressure coupling and reinforcing the underlying physical constraints of the Navier-Stokes equations. Through this, the framework can effectively mitigate training instability and accelerate convergence to achieve accurate solution. Furthermore, a hybrid numerical-automatic differentiation strategy is employed to improve the model's generalizability in resolving flows involving complex geometries. The performance of SIMPLE-PINN is evaluated on a range of challenging benchmark cases, including strongly nonlinear flows, long-term flow prediction, and multiphysics coupling problems. The numerical results demonstrate SIMPLE-PINN's high accuracy and rapid convergence. Notably, SIMPLE-PINN achieves, for the first time, a fully data-free solution of lid-driven cavity flow at Re=20000 in just 448s, and successfully captures the onset and long-time evolution of vortex shedding in flow past a cylinder over t=0-100. These findings demonstrate SIMPLE-PINN's potential as a reliable and competitive neural solver for complex PDEs in intelligent scientific computing, with promising engineering applications in aerospace, civil engineering, and mechanical engineering.

翻译：物理信息神经网络通过将偏微分方程直接嵌入损失函数，在求解偏微分方程方面展现出潜力。尽管取得了显著成功，但现有PINN在应用于强非线性流体动力学问题时，常出现训练不稳定和收敛缓慢的问题。为应对这些挑战，本文提出一种新型PINN框架——SIMPLE-PINN，该框架受半隐式压力关联方程启发，引入了速度和压力校正损失项。这些校正项源自动量和连续性残差，专为PINN框架设计，可确保速度-压力耦合并强化纳维-斯托克斯方程底层的物理约束。通过这种方式，该框架能有效缓解训练不稳定性并加速收敛以实现精确求解。此外，采用混合数值-自动微分策略以提高模型在求解含复杂几何形状流场时的泛化能力。SIMPLE-PINN的性能在一系列具有挑战性的基准算例上得到评估，包括强非线性流动、长期流场预测以及多物理场耦合问题。数值结果表明SIMPLE-PINN具有高精度和快速收敛特性。值得注意的是，SIMPLE-PINN首次在仅448秒内实现了雷诺数Re=20000下顶盖驱动方腔流的完全无数据求解，并成功捕捉了t=0-100时间内圆柱绕流涡脱落的起始与长期演化过程。这些发现表明SIMPLE-PINN作为智能科学计算中复杂偏微分方程的可靠且具有竞争力的神经求解器具有巨大潜力，在航空航天、土木工程和机械工程领域具有广阔工程应用前景。