Heyang Wang

Chang Wei, Yuchen Fan, Jian Cheng Wong et al.

Physics-informed neural networks (PINNs) have emerged as a major research focus. However, today's PINNs encounter several limitations. Firstly, during the construction of the loss function using automatic differentiation, PINNs often neglect information from neighboring points, which hinders their ability to enforce physical constraints and diminishes their accuracy. Furthermore, issues such as instability and poor convergence persist during PINN training, limiting their applicability to complex fluid dynamics problems. To address these challenges, a fast physics-informed neural network framework that integrates a simplified finite volume method (FVM) and residual correction loss term has been proposed, referred to as Fast Finite Volume PINN (FFV-PINN). FFV-PINN utilizes a simplified FVM discretization for the convection term, with an accompanying improvement in the dispersion and dissipation behavior. Unlike traditional FVM, the FFV-PINN outputs can be simply and directly harnessed to approximate values on control surfaces, thereby simplifying the discretization process. Moreover, a residual correction loss term is introduced to significantly accelerates convergence and improves training efficiency. To validate the performance, we solve a series of challenging problems -- including flow in the two-dimensional steady and unsteady lid-driven cavity, three-dimensional steady lid-driven cavity, backward-facing step flows, and natural convection at high Reynolds number and Rayleigh number. Notably, the FFV-PINN can achieve data-free solutions for the lid-driven cavity flow at Re = 10000 and natural convection at Ra = 1e8 for the first time in PINN literature, even while requiring only 680s and 231s. It further highlights the effectiveness of FFV-PINN in improving both speed and accuracy, marking another step forward in the progression of PINNs as competitive neural PDE solvers.

Chang Wei, Yuchen Fan, Chin Chun Ooi et al.

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.