使用物理信息神经网络预测搅拌槽内流动的模型层级
A Model Hierarchy for Predicting the Flow in Stirred Tanks with Physics-Informed Neural Networks
AI总结：
本文探讨了物理信息神经网络（PINNs）作为降阶模型模拟搅拌反应器内流场的潜力，通过强施加边界条件、域分解和XPINN方法构建模型层级，最佳模型在压力和速度上的预测误差小于1%，并展示了跨雷诺数插值的快速评估能力。
摘要：
本文探讨了物理信息神经网络（PINNs）作为降阶模型（ROMs）模拟搅拌反应器（STRs）内流场的潜力。我们在几何复杂的区域内求解二维稳态Navier-Stokes方程，并探索将额外物理见解整合到模型中的方法。这些方法包括强施加Dirichlet边界条件（BCs）和采用域分解（DD），包含重叠和非重叠子域。我们调整了扩展物理信息神经网络（XPINN）方法，基于每个区域内不同的流动特性在不同子域中求解不同的方程组。我们的探索产生了一个跨越不同复杂度级别的模型层级，其中最佳模型的压力和速度的l1预测误差均小于1%。为了说明我们方法的可重复性，我们追踪了最佳识别模型在重复独立训练运行中的误差，并展示了其可靠性。随后，通过将搅拌速率作为参数输入，我们开发了一个快速评估的流动模型，能够在广泛的雷诺数范围内进行插值。尽管我们在本工作中仅限于STRs，但我们得出结论，获得所呈现的模型层级的步骤可以转移到其他应用中。
英文摘要：
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.
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