  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.
