  Time-varying vector fields produced by computational fluid dynamics
simulations are often prohibitively large and pose challenges for accurate
interactive analysis and exploration. To address these challenges, reduced
Lagrangian representations have been increasingly researched as a means to
improve scientific time-varying vector field exploration capabilities. This
paper presents a novel deep neural network-based particle tracing method to
explore time-varying vector fields represented by Lagrangian flow maps. In our
workflow, in situ processing is first utilized to extract Lagrangian flow maps,
and deep neural networks then use the extracted data to learn flow field
behavior. Using a trained model to predict new particle trajectories offers a
fixed small memory footprint and fast inference. To demonstrate and evaluate
the proposed method, we perform an in-depth study of performance using a
well-known analytical data set, the Double Gyre. Our study considers two flow
map extraction strategies as well as the impact of the number of training
samples and integration durations on efficacy, evaluates multiple sampling
options for training and testing and informs hyperparameter settings. Overall,
we find our method requires a fixed memory footprint of 10.5 MB to encode a
Lagrangian representation of a time-varying vector field while maintaining
accuracy. For post hoc analysis, loading the trained model costs only two
seconds, significantly reducing the burden of I/O when reading data for
visualization. Moreover, our parallel implementation can infer one hundred
locations for each of two thousand new pathlines across the entire temporal
resolution in 1.3 seconds using one NVIDIA Titan RTX GPU.
