In this paper, we present a comprehensive evaluation to establish a robust and efficient framework for Lagrangian-based particle tracing using deep neural networks (DNNs). Han et al. (2021) first proposed a DNN-based approach to learn Lagrangian representations and demonstrated accurate particle tracing for an analytic 2D flow field. In this paper, we extend and build upon this prior work in significant ways. First, we evaluate the performance of DNN models to accurately trace particles in various settings, including 2D and 3D time-varying flow fields, flow fields from multiple applications, flow fields with varying complexity, as well as structured and unstructured input data. Second, we conduct an empirical study to inform best practices with respect to particle tracing model architectures, activation functions, and training data structures. Third, we conduct a comparative evaluation of prior techniques that employ flow maps as input for exploratory flow visualization. Specifically, we compare our extended model against its predecessor by Han et al. (2021), as well as the conventional approach that uses triangulation and Barycentric coordinate interpolation. Finally, we consider the integration and adaptation of our particle tracing model with different viewers. We provide an interactive web-based visualization interface by leveraging the efficiencies of our framework, and perform high-fidelity interactive visualization by integrating it with an OSPRay-based viewer. Overall, our experiments demonstrate that using a trained DNN model to predict new particle trajectories requires a low memory footprint and results in rapid inference. Following best practices for large 3D datasets, our deep learning approach using GPUs for inference is shown to require approximately 46 times less memory while being more than 400 times faster than the conventional methods.

翻译：本文提出了一项全面的评估，旨在建立基于深度学习神经网络（DNN）的拉格朗日粒子追踪的稳健高效框架。Han等人（2021）首次提出了一种基于DNN的方法来学习拉格朗日表示，并证明了其在分析二维流场中粒子追踪的准确性。本文在此基础上进行了显著拓展与改进。首先，我们评估了DNN模型在不同场景中精确追踪粒子的性能，包括二维和三维时变流场、来自多种应用的流场、复杂度各异的流场，以及结构化与非结构化输入数据。其次，我们开展了一项实证研究，以指导粒子追踪模型架构、激活函数和训练数据结构的最佳实践。第三，我们对先前使用流图作为输入的探索性流场可视化技术进行了比较评估。具体而言，我们将扩展后的模型与其前身Han等人（2021）的方法以及使用三角剖分和重心坐标插值的传统方法进行了对比。最后，我们考虑了粒子追踪模型与不同查看器的集成与适配。通过利用本框架的高效性，我们提供了一个基于网络的交互式可视化界面，并通过将其与基于OSPRay的查看器集成，实现了高保真交互式可视化。总体而言，实验表明，使用训练后的DNN模型预测新粒子轨迹只需较低的内存占用，并能实现快速推理。针对大型三维数据集的最佳实践表明，我们的深度学习推理方法（使用GPU）所需内存约为传统方法的1/46，而速度则比传统方法快400倍以上。