# Accelerated Probabilistic Marching Cubes by Deep Learning for Time-Varying Scalar Ensembles

arXiv: https://arxiv.org/abs/2207.07260 · HTML: https://mlsanity.com/paper/2207.07260/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 15 Jul 2022.

## Builds on (most cited first, 10 of 10)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Compressive Neural Representations of Volumetric Scalar Fields](https://mlsanity.com/paper/2104.04523/) (2021)
- [InSituNet: Deep Image Synthesis for Parameter Space Exploration of Ensemble Simulations](https://mlsanity.com/paper/1908.00407/) (2019)
- [DL4SciVis: A State-of-the-Art Survey on Deep Learning for Scientific Visualization](https://mlsanity.com/paper/2204.06504/) (2022)
- [A Generative Model for Volume Rendering](https://mlsanity.com/paper/1710.09545/) (2017)
- [A Survey on ML4VIS: Applying Machine Learning Advances to Data Visualization](https://mlsanity.com/paper/2012.00467/) (2020)
- [Exploratory Lagrangian-Based Particle Tracing Using Deep Learning](https://mlsanity.com/paper/2110.08338/) (2021)
- [Uncertainty-Oriented Ensemble Data Visualization and Exploration using Variable Spatial Spreading](https://mlsanity.com/paper/2011.01497/) (2020)
- [Uncertainty Visualization of the Marching Squares and Marching Cubes Topology Cases](https://mlsanity.com/paper/2108.03066/) (2021)

## Built on by (most cited first, 3 of 3)

- [REV-INR: Regularized Evidential Implicit Neural Representation for Uncertainty-Aware Volume Visualization](https://mlsanity.com/paper/2601.17689/) (2026)
- [Efficient Probabilistic Visualization of Local Divergence of 2D Vector Fields with Independent Gaussian Uncertainty](https://mlsanity.com/paper/2510.01190/) (2025)
- [Efficient Level-Crossing Probability Calculation for Gaussian Process Modeled Data](https://mlsanity.com/paper/2512.12442/) (2025)

## Abstract (arXiv)

Visualizing the uncertainty of ensemble simulations is challenging due to the large size and multivariate and temporal features of ensemble data sets. One popular approach to studying the uncertainty of ensembles is analyzing the positional uncertainty of the level sets. Probabilistic marching cubes is a technique that performs Monte Carlo sampling of multivariate Gaussian noise distributions for positional uncertainty visualization of level sets. However, the technique suffers from high computational time, making interactive visualization and analysis impossible to achieve. This paper introduces a deep-learning-based approach to learning the level-set uncertainty for two-dimensional ensemble data with a multivariate Gaussian noise assumption. We train the model using the first few time steps from time-varying ensemble data in our workflow. We demonstrate that our trained model accurately infers uncertainty in level sets for new time steps and is up to 170X faster than that of the original probabilistic model with serial computation and 10X faster than that of the original parallel computation.