My research focuses on visualization and analysis of complex and/or large-scale multidimensional data sets, e.g. micro-computed/synchrotron tomography, simulation parameter spaces, surrogate models, etc. The tool I use is tensor decompositions (mostly the tensor train (TT), the Tucker model, and other tensor networks): they lend themselves very well to data manipulation in the compressed domain, including derivation/integration, convolution, element-wise operations, statistical moments, etc. I used these in my PhD for multidimensional compression, filtering, surrogate modeling, sensitivity analysis, and feature extraction, among others.
Related techniques include 3D/4D multiresolution representations, progressive tensor rank reconstruction and out-of-core memory management.
More details on the scientific visualization aspect:
More details on surrogate modeling/high-dimensional learning:
- Tensor Algorithms for Advanced Sensitivity Metrics (2018, accepted)
- Tensor Decompositions for Integral Histogram Compression and Look-Up (2018)
- Multiresolution Volume Filtering in the Tensor Compressed Domain (2017)
- A Surrogate Visualization Model Using the Tensor Train Format (2016)
- Compressing Bidirectional Texture Functions via Tensor Train Decomposition (2016)
- Analysis of Tensor Approximation for Compression-Domain Volume Visualization (2015)
- Lossy Volume Compression Using Tucker Truncation and Thresholding (2015)
- TTHRESH: Tensor Compression for Multidimensional Visual Data
- Sobol Tensor Trains for Global Sensitivity Analysis (arXiv, 2017)