标题： FlexPINN：使用灵活的物理信息神经网络建模三维微混合器几何中的流体动力学和质量传递 显示英文标题

标题： FlexPINN: Modeling Fluid Dynamics and Mass Transfer in 3D Micromixer Geometries Using a Flexible Physics-Informed Neural Network

摘要： 在这项研究中，使用了一种具有改进的物理信息神经网络（FlexPINN）来研究带有不同形状和配置鳍片的三维T形微混合器内部的流体流动和浓度分布，该方法包括对标准PINN架构的修改。 考虑了三种类型的鳍片（矩形、椭圆形和三角形），以评估鳍片几何形状的影响，并结合三维通道内的四种不同鳍片配置来研究位置的影响。 模拟是在四个雷诺数下进行的：5、20、40 和 80，在单单元（四个鳍片）和双单元（八个鳍片）配置中均进行了测试。 目标是利用FlexPINN方法评估压力降系数、混合指数和混合效率。 鉴于用标准PINN模拟三维问题的挑战，引入了几项改进措施。 控制方程被注入网络作为一阶无量纲导数，以提高准确性。 转移学习用于减少计算成本，自适应损失加权用于提高收敛性，与标准PINN方法相比。 这些修改使得可以跨多个测试案例使用一致且灵活的架构。 使用所提出的FlexPINN方法，与计算流体力学（CFD）结果相比，预测的压力降系数和混合指数的最大误差分别为3.25%和2.86%。 在所有测试案例中，在雷诺数为40的双单元设置中配置C的矩形鳍片表现出最高的混合效率，达到1.63的值。 FlexPINN框架在模拟复杂三维几何形状中的流体流动和物质传输方面表现出强大的能力。 显示英文摘要

摘要： In this study, fluid flow and concentration distribution inside a 3D T-shaped micromixer with various fin shapes and configurations are investigated using a Flexible Physics-Informed Neural Network (FlexPINN), which includes modifications over the vanilla PINN architecture. Three types of fins (rectangular, elliptical, and triangular) are considered to evaluate the influence of fin geometry, along with four different fin configurations inside the 3D channel to examine the effect of placement. The simulations are conducted at four Reynolds numbers: 5, 20, 40, and 80, in both single-unit (four fins) and double-unit (eight fins) configurations. The goal is to assess pressure drop coefficient, mixing index, and mixing efficiency using the FlexPINN method. Given the challenges in simulating 3D problems with standard PINN, several improvements are introduced. The governing equations are injected into the network as first-order, dimensionless derivatives to enhance accuracy. Transfer learning is used to reduce computational cost, and adaptive loss weighting is applied to improve convergence compared to the vanilla PINN approach. These modifications enable a consistent and flexible architecture that can be used across numerous tested cases. Using the proposed FlexPINN method, the pressure drop coefficient and mixing index are predicted with maximum errors of 3.25% and 2.86%, respectively, compared to Computational Fluid Dynamics (CFD) results. Among all the tested cases, the rectangular fin with configuration C in the double-unit setup at Reynolds number 40 shows the highest mixing efficiency, reaching a value of 1.63. The FlexPINN framework demonstrates strong capabilities in simulating fluid flow and species transport in complex 3D geometries.