近些年来物理神经网络(PINN)在计算流体动力学模拟中的应用引起了广泛关注。在传统PINN的模拟中，配置点的布置需要考虑固体边界的位置，不利于处理复杂固体边界问题。本文提出了一种结合直接力浸入边界(IB)方法的新型PINN方法。在提出的IB-PINN中，消除了布置配置点时的边界一致性要求。同时，在损失函数中加入标记点处的速度惩罚损失，以满足流固界面处的无滑移条件。此外，在损失函数中还加入了部分配置点处的力惩罚损失，以保证体积力的紧致分布。

    首先，通过对在槽道中圆柱的层流流动模拟，证明了IB-PINN在求解不可压缩Navier-Stokes方程中的有效性。将采用IB-PINN方法得到的解与传统基于网格的IB方法和基于贴体网格的有限体积方法得到的参考解进行了比较。结果表明，这三种方法得到的结果是非常一致的。此外，我们还研究了深度神经网络（DNN）结构、Adam训练次数、总损失不同部分的权重、配置点和标记点的个数、体积力紧致约束条件、配置点取样方式、方程形式和输入变量形式对IB-PINN性能的影响。

    其次，利用迁移学习，对不同雷诺数下，不同形状的固体绕流问题进行了研究。针对不同雷诺数的流动进行了迁移学习，以求解雷诺数40的流动时训练得到的DNN作为基准DNN，分别对雷诺数为10、20、30的工况进行迁移学习，发现与雷诺数40越近，迁移学习的效果越好。同时讨论了取点间距 h=0.05 情况下的计算准确度以及计算所需时间，发现在保证可接受准确度的前提下能够大大减少计算时间。针对不同固体形状绕流的迁移学习中，首先对浸入形状曲线进行建模，先在一定范围内生成随机控制点，在相邻控制点间生成贝塞尔曲线，进而组合形成固体边界的形状曲线，并以圆柱绕流算例训练得到的DNN为基准DNN，对生成的不同固体边界绕流问题进行迁移学习。训练结果表明，IB-PINN有着较好的迁移学习性能，使得DNN再训练的收敛过程加速，在相近形状下迁移学习较原始学习能够加速80%左右。

    In recent years, the application of physis-informed neural networks (PINN) in computational fluid dynamics simulation has attracted much attention. In PINN simulation, the collocation points are required to conform to the fluid-solid interface under the condition of no-slip boundary. In this paper, a novel PINN method combined with the direct-force immersed boundary (IB) method is proposed. In the proposed IB-PINN, the boundary consistency requirement for collocation points is eliminated. Instead, the velocity penalty loss at marked points is added to the loss function to strengthen the no-slip condition of the fluid-solid interface. In addition, the force penalty loss at some ccollocation points is added to the loss function to ensure the compact distribution of the volume force.

    The effectiveness of IB-PINN in solving incompressible Navier-Stokes equations is demonstrated by simulating laminar flow in a circular cylinder placed in a channel. The solution obtained by IB-PINN method is compared with the reference solution obtained by traditional grid-based IB method and Fluent method. The comparison shows that the results obtained by these three solutions are very consistent. In addition, the effects of DNN structure, Adam training iterations, weight of different components of total loss, number of collocation points and marker points, volume force compaction constraints, sampling method of collocation points, equation form and input variable form on IB-PINN performance are also studied.

    Transfer learning experiments are carried out to solve Navier-Stokes equations with different Reynolds numbers and different immersed object shapes. In the transfer learning with different Reynolds numbers, the DNN trained with Reynolds number 40 is used as the baseline DNN, and the transfer learning is carried out with Reynolds number 10, 20, and 30, respectively. It is found that the closer the Reynolds number is to 40, the better the transfer learning effect is. At the same time, At the same time, the calculation accuracy and calculation time are discussed when the point spacing h=0.05, and it is found that the calculation time can be greatly reduced on the premise of ensuring acceptable accuracy. For the transfer learning of flows around different solid shapes, the immersed shape curve is modeled first, and the random control points are generated within a certain rangeIn the transfer learning of different shapes, and Bessel curves are generated between adjacent control points, and then combined to form solid boundary shape curves. DNN, which is obtained by training of cylindrical flow around the example, is taken as the benchmark DNN. The training results show that, IB-PINN has good transfer learning performance, which accelerates the convergence process of DNN retraining. Transfer learning can accelerate about 80% compared with original learning under similar shapes.