In many practical fluid dynamics experiments, measuring variables such as velocity and pressure is possible only at a limited number of sensor locations, \textcolor{black}{for a few two-dimensional planes, or for a small 3D domain in the flow}. However, knowledge of the full fields is necessary to understand the dynamics of many flows. Deep learning reconstruction of full flow fields from sparse measurements has recently garnered significant research interest, as a way of overcoming this limitation. This task is referred to as the flow reconstruction (FR) task. In the present study, we propose a convolutional autoencoder based neural network model, dubbed FR3D, which enables FR to be carried out for three-dimensional flows around extruded 3D objects with different cross-sections. An innovative mapping approach, whereby multiple fluid domains are mapped to an annulus, enables FR3D to generalize its performance to objects not encountered during training. We conclusively demonstrate this generalization capability using a dataset composed of 80 training and 20 testing geometries, all randomly generated. We show that the FR3D model reconstructs pressure and velocity components with a few percentage points of error. Additionally, using these predictions, we accurately estimate the Q-criterion fields as well lift and drag forces on the geometries.

翻译：在许多实际流体动力学实验中，仅能在有限传感器位置、少数二维平面或小型三维流场域内测量速度和压力等变量。然而，理解众多流动的动力学特性需要掌握完整的流场信息。近年来，通过深度学习从稀疏测量中重建完整流场（即流场重建任务FR）已成为突破该限制的重要研究方向。本研究提出一种基于卷积自编码器的神经网络模型FR3D，能够对不同截面形状的三维挤出物体进行三维流场重建。通过创新性映射方法将多个流体域映射到环形区域，该模型可泛化应用于训练中未出现的物体构型。我们采用由80个训练几何体与20个测试几何体构成的随机生成数据集，有力验证了这种泛化能力。结果表明，FR3D模型重建的压力与速度分量误差仅为几个百分点。此外，基于这些预测值，我们能够准确估算Q准则场以及几何体的升力和阻力。