Interactive Visualization of Time-Varying Flow Fields Using Particle Tracing Neural Networks

TL;DR

This work addresses the heavy computational cost of visualizing time-varying flows by learning Lagrangian flow maps with particle-tracing neural networks. Building on prior 2D MLP approaches, it extends to 2D/3D flows, structured/unstructured data, and interactive viewers, while systematically evaluating network architecture, activation functions, and training data strategies. The authors demonstrate that sinusoidal activations and a Lagrangian_hybrid data generation strategy yield higher accuracy and better domain coverage, and show that model pruning and GPU-based inference yield substantial speedups and memory reductions (e.g., ~46x memory and ~400x speedups over conventional methods). They also integrate web-based and OSPRay viewers to enable practical post hoc exploration, highlighting significant improvements in interactivity for large-scale 3D datasets, with plans to tackle unstructured data challenges and long trajectories in future work.

Abstract

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.

Figures (9)

• Figure 1: The workflow of our deep learning-based particle tracing model. The Lagrangian flow maps are created using in situ processing, saved to the database, and input into a neural network to learn the corresponding end locations based on particle start locations and file cycles. Once the model has been fully trained, new particle trajectories can be inferred from the model and visualized using the developed viewer.
• Figure 2: Illustration for $Lagrangian_{long}$, $Lagrangian_{short}$ and $Lagrangian_{hybird}$ methods using 1D particle trajectories. The x-axis represents the file cycle. Circles with the same color have the same labels. The $Lagrangian_{long}$ extracts a single flow map with end locations at uniform time intervals along the trajectories. In contrast, the $Lagrangian_{short}$ extracts several short flow maps, resetting start seeds for each time interval. The $Lagrangian_{hybird}$ combines the strengths of both $Lagrangian_{long}$ and $Lagrangian_{short}$: it extracts the $Lagrangian_{short}$ flow maps, where each individual flow map follows the structure of a $Lagrangian_{long}$ flow map. $Lagrangian_{hybird}$ achieves both comprehensive domain coverage and comparable accuracy.
• Figure 3: The MLP architecture of our neural network. The network architecture begins by taking two inputs: the particle's initial location (Start) and the number of file cycles (File Cycle). These inputs are first processed by the Encoder, which transforms them into a latent vector represented as $D_{in}$. Following this, the latent vector $D_{in}$ is input into the Decoder. The Decoder then processes this information to output the final location (End) of the particle at the queried file cycle. The sinusoidal activation function is used after the FC layers in the model except the output layer.
• Figure 4: The error plot compares our sinusodial-based MLP with the ReLU-based MLP of Han et al. han2021exploratory. The sinusoidal activation function improves the inference accuracy significantly.
• Figure 5: Violin plot depicting the inference errors for models trained on Gerris Flow dataset with varying Reynolds numbers, using either the $Lagrangian_{long}$ method with one or two models or the $Lagrangian_{hybrid}$ method with one or two models. These evaluations, conducted with $5,000$ testing seeds, calculate errors following \ref{['eqn:error']}. A comparison of violin plots of the same color across different datasets reveals that errors tend to increase as the flow behavior becomes more turbulent. Interestingly, using fewer flow maps for training in the $Lagrangian_{long}$ approach does not improve accuracy. Conversely, in the $Lagrangian_{hybrid}$ approach, using fewer flow maps actually led to a slight decrease in median errors. Furthermore, the $Lagrangian_{hybrid}$ method effectively reduces error propagation while maintaining domain coverage.