This paper explores the potential of Physics-Informed Neural Networks (PINNs) to serve as Reduced Order Models (ROMs) for simulating the flow field within stirred tank reactors (STRs). We solve the two-dimensional stationary Navier-Stokes equations within a geometrically intricate domain and explore methodologies that allow us to integrate additional physical insights into the model. These approaches include imposing the Dirichlet boundary conditions (BCs) strongly and employing domain decomposition (DD), with both overlapping and non-overlapping subdomains. We adapt the Extended Physics-Informed Neural Network (XPINN) approach to solve different sets of equations in distinct subdomains based on the diverse flow characteristics present in each region. Our exploration results in a hierarchy of models spanning various levels of complexity, where the best models exhibit l1 prediction errors of less than 1% for both pressure and velocity. To illustrate the reproducibility of our approach, we track the errors over repeated independent training runs of the best identified model and show its reliability. Subsequently, by incorporating the stirring rate as a parametric input, we develop a fast-to-evaluate model of the flow capable of interpolating across a wide range of Reynolds numbers. Although we exclusively restrict ourselves to STRs in this work, we conclude that the steps taken to obtain the presented model hierarchy can be transferred to other applications.

翻译：本文探讨了物理信息神经网络作为降阶模型在搅拌釜反应器流场模拟中的应用潜力。我们求解了几何复杂域内的二维稳态纳维-斯托克斯方程，并探索了将额外物理知识融入模型的方法体系，包括强施加狄利克雷边界条件以及采用重叠与非重叠子区域的域分解策略。我们改进了扩展物理信息神经网络方法，依据各子区域不同的流动特性求解不同方程集。研究构建了涵盖多级复杂度的模型层次体系，其中最优模型对压力和速度的l1预测误差均低于1%。为验证方法的可重复性，我们追踪了最优模型在多次独立重复训练中的误差变化，证明了其可靠性。随后，通过将搅拌速率作为参数化输入，我们开发了能够跨雷诺数范围进行插值的快速流场预测模型。尽管本文仅聚焦于搅拌釜反应器，但所提出的模型层次构建方法具有可迁移至其他应用的普适性。