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 against 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 the best practices for large 3D datasets, our deep learning approach 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评估，旨在建立基于深度神经网络（DNN）的拉格朗日粒子追踪稳健高效框架。Han等人（2021）首次提出基于DNN的学习拉格朗日表示方法，并展示了在二维解析流场中的精确粒子追踪。本研究在以下方面对此前工作进行了显著拓展与深化：首先，我们评估了DNN模型在多种场景下精确追踪粒子的性能，包括二维与三维时变流场、多应用场景流场、不同复杂度流场，以及结构化与非结构化输入数据；其次，通过实证研究确定了粒子追踪模型架构、激活函数与训练数据结构的优化实践；第三，我们与使用流图作为输入的探索性流可视化先验技术进行了对比评估，具体将扩展模型与Han等人（2021）的前期工作及采用三角剖分和重心坐标插值的传统方法进行了比较；最后，我们探讨了粒子追踪模型与不同可视化系统的集成适配。通过利用框架的高效性，我们开发了基于Web的交互式可视化界面，并与基于OSP Ray的可视化系统集成实现了高保真交互可视化。整体实验表明，使用训练后的DNN模型预测新粒子轨迹所需内存占用低且推理速度极快。针对大规模三维数据集的优化实践显示，与传统方法相比，本文的深度学习方法内存需求量降低约46倍，速度提升超过400倍。