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Research Highlight

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

Topic:

Achievement: Understanding the uncertainty of scientific data and visualizations is of paramount importance for researchers to avoid misleading interpretations and improve trust in scientific discoveries. Probabilistic marching cubes algorithm [1] is a technique to understand the positional uncertainty of level sets of scientific data. Although the technique has gained popularity in the last decade due to its effectiveness in conveying uncertainty, the high computational cost of the probabilistic marching cubes algorithm limits interactivity of visualization applications, and hence increases the time to scientific insight. We propose a novel deep learning method that achieves 170X average speed up compared to the original probabilistic marching cubes algorithm [1] implementation and performs predictions with an accuracy comparable to the original algorithm. The acceleration achieved with our proposed approach enables scientists analyze the uncertainty of level-sets without compromising the performance of visualization applications.

Significance and Impact: Although there have been significant advances in uncertainty quantification and visualization research over the past two decades, only a few research has addressed the challenge of minimizing computational overhead caused by integrating uncertainty into data analysis. In this paper, we demonstrate how machine learning may effectively be leveraged to accelerate the uncertainty analysis of scientific data through a use case of level sets for time-varying ensembles. The approach presented in this paper opens a new research opportunity for scientific community to effectively leverage machine learning for efficient uncertainty analysis of scientific data across diverse domains.

Research Details

  • The uncertainty in time-varying ensemble data is estimated per grid cell by fitting multivariate Gaussian distributions to data similar to the probabilistic marching cubes algorithm [1].
  • For time-varying ensembles, the initial few time steps are used to gather training data. The training data for our deep learning model comprised a mapping from mean and covariance matrix describing a multivariate Gaussian distribution and isovalue to a level-crossing probability computed using the Monte Carlo approach proposed in the original probabilistic marching cubes paper [1]. 
  • The trained model is then used to efficiently predict level-crossing probabilities for remaining time steps of the time-varying ensemble simulation (170X average speed up compared to the Monte Carlo sampling approach using serial code).
  • Level-crossing probabilities are conveyed to users via color mapping similar to the original probabilistic marching cubes paper.

Facility: Visualization Group at ORNL.

Sponsor/Funding: Scientific Discovery Through Advanced Computing program in the U.S. Department of Energy (DOE SciDAC), Intel Graphics and Visualization Institutes of XeLLENCE, the Intel OneAPI CoE, National Institutes of Health (NIH), and Utah Office of Energy Development

PI and affiliation: David Pugmire, Visualization Group, Computer Science and Mathematics Division, ORNL, 
Chris R. Johnson, Distinguished Professor, SCI Institute, University of Utah
Team: Mengjiao Han (SCI Institute, University of Utah), Tushar M. Athawale (ORNL), David Pugmire (ORNL), Chris R. Johnson (SCI Institute, University of Utah)

Citation and DOI: Mengjiao Han, Tushar M. Athawale, David Pugmire, Chris R. Johnson, Accelerated Probabilistic Marching Cubes by Deep Learning for Time-Varying Scalar Ensembles. In IEEE VIS 2022 Conference: Short Papers, Oklahoma City, Oklahoma, 2022. [pdf] [Acceptance rate: 33/104 = 32%]

Accelerated Probabilistic Marching Cubes by Deep Learning for Time-Varying Scalar Ensembles
Efficient visualization of level-crossing probabilities (isovalue = 0.1) for the Red Sea velocity magnitude data set (https://kaust-vislab.github.io/SciVis2020/data.html) using our proposed neural network. Image (a) shows level-crossing probabilities computed using the original probabilistic marching cubes algorithm [1]. Image (b) shows the result computed by our machine learning model, which is visually indistinguishable from image (a). The zoomed-in views are displayed in the top right for images (a) and (b). The parallel computation achieves an average speed up of 17X compared to the serial implementation of the original probabilistic marching cubes algorithm [image (c)], and our machine learning approach achieves an average speed up of 10X compared to parallel computations [image (d)].

Summary: 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.

[1] K. P thkow, B. Weber, and H.-C. Hege. Probabilistic Marching Cubes. Computer Graphics Forum, vol. 30, no. 3, pp. 931-940. Wiley Online Library, 2011.