FFV-PINN: A Fast Physics-Informed Neural Network with Simplified Finite Volume Discretization and Residual Correction

作者：Chang Wei, Yuchen Fan, Jian Cheng Wong, C. Ooi, Heyang Wang, P. Chiu · 发表于：Computer Methods in Applied Mechanics and Engineering · 年份：2025 · DOI：10.1016/j.cma.2025.118139 · 被引用次数：26 · 研究领域：Computer Science

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 Raylei...