High-dimensional Data Analysis and Visualization

High-dimensional Data Analysis and Visualization

High-dimensional Data Analysis and Visualization: Understanding and describing expensive black box functions such as physical simulations is a common problem in many application areas. One example is the recent interest in uncertainty quantification with the goal of discovering the relationship between a potentially large number of input parameters and the output of a simulation. We model large-scale physical simulation datasets as a high-dimensional scalar function defined over a discrete sample of the domain. First, we provide structural analysis of such a function at multiple scales and provide
insight into the relationship between the input parameters and the output. Second, we enable exploratory analysis for users, where we help the users to differentiate features from noise through multi-scale analysis on an interactive platform, based on domain knowledge and data characterization. Our analysis is performed by exploiting the topological and geometric properties of the domain, building statistical models based on its topological segmentations and providing interactive visual interfaces to facilitate such explorations.

Adaptive Sampling: Dynamic Probabilistic Risk Assessment (PRA) and uncertainty quantification (UQ) of complex systems such as nuclear simulations usually employ sampling algorithms which perform series of computationally expensive simulation runs given a large set of uncertainty parameters. Consequently, the space of the possible solutions, the response surface, can be sampled only very sparsely and this precludes the ability to fully analyze the impact of uncertainties on the system dynamics. Adaptive sampling algorithms aim to overcome these limitations by sampling unexplored and risk-significant regions of the response surface. They infer system responses from surrogate models constructed from existing samples and suggest the most relevant location of the next sample. We aim to develop advanced adaptive sampling techniques to understand the response space locally and globally, drawing inspirations from topology, geometry and machine learning. 

 

Recent publications:

* Exploration of High-Dimensional Scalar Function for Nuclear Reactor
Safety Analysis and Visualization.
Dan Maljovec, Bei Wang, Valerio Pascucci, Peer-Timo Bremer, Michael
Pernice, Diego Mandelli and Robert Nourgaliev.
Proceedings International Conference on Mathematics and Computational
Methods Applied to Nuclear Science & Engineering (M&C) , pages
712-723, 2013.
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* Adaptive Sampling Algorithms for Probabilistic Risk Assessment of
Nuclear Simulations.
Dan Maljovec, Bei Wang, Diego Mandelli, Peer-Timo Bremer and Valerio Pascucci.
International Topical Meeting on Probabilistic Safety Assessment and
Analysis (PSA) (accepted), 2013.
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* Analyze Dynamic Probabilistic Risk Assessment Data through Clustering.
Dan Maljovec, Bei Wang, Diego Mandelli, Peer-Timo Bremer and Valerio Pascucci.
International Topical Meeting on Probabilistic Safety Assessment and
Analysis (PSA) (Accepted), 2013.
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* Branching and Circular Features in High Dimensional Data.
Bei Wang, Brian Summa, Valerio Pascucci and Mikael Vejdemo-Johansson
IEEE Transactions on Visualization and Computer Graphics , 17(12),
pages 1902-1911, 2011.
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* Visual Exploration of High Dimensional Scalar Functions .
Samuel Gerber, Peer-Timo Bremer, Valerio Pascucci, and Ross Whitaker.
IEEE Transactions on Visualization and Computer Graphics 16(6), pp.
1271-1280, 2010.
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