A Bayesian fusion model for space-time reconstruction of finely resolved velocities in turbulent flows from low resolution measurements

The study of turbulent flows calls for measurements with high resolution both in space and in time. We propose a new approach to reconstruct High-Temporal-High-Spatial resolution velocity fields by combining two sources of information that are well-resolved either in space or in time, the Low-Temporal-High-Spatial (LTHS) and the High-Temporal-Low-Spatial (HTLS) resolution measurements. In the framework of co-conception between sensing and data post-processing, this work extensively investigates a Bayesian reconstruction approach using a simulated database. A Bayesian fusion model is developed to solve the inverse problem of data reconstruction. The model uses a Maximum A Posteriori estimate, which yields the most probable field knowing the measurements. The DNS of a wall-bounded turbulent flow at moderate Reynolds number is used to validate and assess the performances of the present approach. Low resolution measurements are subsampled in time and space from the fully resolved data. Reconstructed velocities are compared to the reference DNS to estimate the reconstruction errors. The model is compared to other conventional methods such as Linear Stochastic Estimation and cubic spline interpolation. Results show the superior accuracy of the proposed method in all configurations. Further investigations of model performances on various range of scales demonstrate its robustness. Numerical experiments also permit to estimate the expected maximum information level corresponding to limitations of experimental instruments.Comment: 15 pages, 6 figure

Visualization-driven Structural and Statistical Analysis of Turbulent Flows

Knowledge extraction from data volumes of ever increasing size requires ever more flexible tools to facilitate interactive query. In- teractivity enables real-time hypothesis testing and scientific discovery, but can generally not be achieved without some level of data reduction. The approach described in this paper combines multi-resolution access, region-of-interest extraction, and structure identification in order to pro- vide interactive spatial and statistical analysis of a terascale data volume. Unique aspects of our approach include the incorporation of both local and global statistics of the flow structures, and iterative refinement fa- cilities, which combine geometry, topology, and statistics to allow the user to effectively tailor the analysis and visualization to the science. Working together, these facilities allow a user to focus the spatial scale and domain of the analysis and perform an appropriately tailored mul- tivariate visualization of the corresponding data. All of these ideas and algorithms are instantiated in a deployed visualization and analysis tool called VAPOR, which is in routine use by scientists internationally. In data from a 10243 simulation of a forced turbulent flow, VAPOR allowed us to perform a visual data exploration of the flow properties at interac- tive speeds, leading to the discovery of novel scientific properties of the flow, in the form of two distinct vortical structure populations. These structures would have been very difficult (if not impossible) to find with statistical overviews or other existing visualization-driven analysis ap- proaches. This kind of intelligent, focused analysis/refinement approach will become even more important as computational science moves to- wards petascale applications

Multivariate Pointwise Information-Driven Data Sampling and Visualization

With increasing computing capabilities of modern supercomputers, the size of the data generated from the scientific simulations is growing rapidly. As a result, application scientists need effective data summarization techniques that can reduce large-scale multivariate spatiotemporal data sets while preserving the important data properties so that the reduced data can answer domain-specific queries involving multiple variables with sufficient accuracy. While analyzing complex scientific events, domain experts often analyze and visualize two or more variables together to obtain a better understanding of the characteristics of the data features. Therefore, data summarization techniques are required to analyze multi-variable relationships in detail and then perform data reduction such that the important features involving multiple variables are preserved in the reduced data. To achieve this, in this work, we propose a data sub-sampling algorithm for performing statistical data summarization that leverages pointwise information theoretic measures to quantify the statistical association of data points considering multiple variables and generates a sub-sampled data that preserves the statistical association among multi-variables. Using such reduced sampled data, we show that multivariate feature query and analysis can be done effectively. The efficacy of the proposed multivariate association driven sampling algorithm is presented by applying it on several scientific data sets.Comment: 25 page