# Exploratory Lagrangian-Based Particle Tracing Using Deep Learning

arXiv: https://arxiv.org/abs/2110.08338 · HTML: https://mlsanity.com/paper/2110.08338/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 67 references that are in the map.
- First posted on arXiv 15 Oct 2021.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [InSituNet: Deep Image Synthesis for Parameter Space Exploration of Ensemble Simulations](https://mlsanity.com/paper/1908.00407/) (2019)
- [A Generative Model for Volume Rendering](https://mlsanity.com/paper/1710.09545/) (2017)
- [Volumetric Isosurface Rendering with Deep Learning-Based Super-Resolution](https://mlsanity.com/paper/1906.06520/) (2019)
- [Deep Volumetric Ambient Occlusion](https://mlsanity.com/paper/2008.08345/) (2020)
- [EddyNet: A Deep Neural Network For Pixel-Wise Classification of Oceanic Eddies](https://mlsanity.com/paper/1711.03954/) (2017)
- [Robust Reference Frame Extraction from Unsteady 2D Vector Fields with Convolutional Neural Networks](https://mlsanity.com/paper/1903.10255/) (2019)
- [Void-and-Cluster Sampling of Large Scattered Data and Trajectories](https://mlsanity.com/paper/1907.05073/) (2019)
- [Coherent structure coloring: identification of coherent structures from sparse data using graph theory](https://mlsanity.com/paper/1610.00197/) (2016)
- [Scalable In Situ Lagrangian Flow Map Extraction: Demonstrating the Viability of a Communication-Free Model](https://mlsanity.com/paper/2004.02003/) (2020)

## Built on by (most cited first, 7 of 7)

- [DL4SciVis: A State-of-the-Art Survey on Deep Learning for Scientific Visualization](https://mlsanity.com/paper/2204.06504/) (2022)
- [PSRFlow: Probabilistic Super Resolution with Flow-Based Models for Scientific Data](https://mlsanity.com/paper/2308.04605/) (2023)
- [ParamsDrag: Interactive Parameter Space Exploration via Image-Space Dragging](https://mlsanity.com/paper/2407.14100/) (2024)
- [A DNN Framework for Learning Lagrangian Drift With Uncertainty](https://mlsanity.com/paper/2204.05891/) (2022)
- [Accelerated Probabilistic Marching Cubes by Deep Learning for Time-Varying Scalar Ensembles](https://mlsanity.com/paper/2207.07260/) (2022)
- [VortexViz: Finding Vortex Boundaries by Learning from Particle Trajectories](https://mlsanity.com/paper/2404.01352/) (2024)
- [Uncertainty Tube Visualization of Particle Trajectories](https://mlsanity.com/paper/2508.13505/) (2025)

## Abstract (arXiv)

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.