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：本文提出了一种全面评估方法，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学习拉格朗日表示的方法，并在解析二维流场中实现了精确的粒子追踪。本文在此基础上进行了重要扩展与改进：首先，系统评估了DNN模型在多种场景中精确追踪粒子的性能，包括二维及三维时变流场、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，通过实证研究总结了粒子追踪模型架构、激活函数及训练数据结构的最佳实践。第三，对先前采用流场映射作为输入的探索性流场可视化技术进行了对比评估，具体包括将扩展模型与其前身（Han等人，2021）以及基于三角剖分和重心坐标插值的传统方法进行对比。最后，探讨了粒子追踪模型与不同可视化系统的集成与适配方案。通过利用框架的高效性，我们开发了基于网页的交互式可视化界面，并通过集成OSPRay渲染器实现了高保真交互式可视化。实验结果表明，使用训练后的DNN模型预测新粒子轨迹具有低内存占用和快速推理能力。针对大规模三维数据集的最佳实践表明，采用GPU进行推理的深度学习方法相比传统方法内存占用减少约46倍，速度提升超过400倍。