A wide range of problems in applied physics and engineering involve learning physical displacement fields from data. In this paper we propose a deep neural network-based approach for learning displacement fields in an end-to-end manner, focusing on the specific case of particle image velocimetry (PIV), a key approach in experimental fluid dynamics that is of crucial importance in diverse applications such as automotive, aerospace and biomedical engineering. The current state of the art in PIV data processing involves traditional handcrafted models that are subject to limitations including the substantial manual effort required and difficulties in generalizing across conditions. By contrast, the deep learning-based approach introduced in this paper, which is based on a recent optical flow learning architecture known as recurrent all-pairs field transforms, is general, largely automated and provides high spatial resolution. Extensive experiments, including benchmark examples where true gold standards are available for comparison, demonstrate that the proposed approach achieves state-of-the-art accuracy and generalization to new data, relative to both classical approaches and previously proposed optical flow learning schemes.

应用物理和工程中的广泛问题涉及从数据中学习物理位移场。在本文中，我们提出了一种基于深度神经网络的方法，用于以端到端的方式学习位移场，重点关注粒子图像测速 (PIV) 的具体情况，这是实验流体动力学中至关重要的一种关键方法在汽车、航空航天和生物医学工程等多种应用中。PIV 数据处理的当前技术水平涉及传统的手工模型，这些模型受到限制，包括所需的大量手动工作和跨条件概括的困难。相比之下，本文介绍的基于深度学习的方法，它基于最近称为循环全对场变换的光流学习架构，具有通用性、高度自动化并提供高空间分辨率。广泛的实验，包括可用于比较的真正黄金标准的基准示例，表明所提出的方法相对于经典方法和先前提出的光流学习方案，实现了最先进的准确性和对新数据的泛化。