We contribute the first algorithm that can extract the full set of Sobol indices from a tensor surrogate model, as well as many other advanced sensitivity metrics. This allows us, among others, to measure interactions of arbitrary order between input variables of complex systems.
We propose a 3D/4D compression algorithm that exploits the Tucker decomposition, together with bit-plane and arithmetic coding, to achieve extreme compression rates in real-world data sets such as tomographic scans and turbulent physical simulations.
We develop GPU-accelerated algorithms for lar-ge tensors that enable efficient level-of-detail rendering and signal processing operations of gigabyte-scale volume data sets: 3D convolution, denoising, computing histograms, progressive reconstruction, etc.
My research interests include scientific visualization, sensitivity analysis, tensor decompositions, and surrogate modeling.
We model and visualize multidimensional para-meter spaces (physical simulations, dynamical systems, reaction networks) using the tensor train decomposition. Users can interactively reduce the model's dimensionality, explore it, and extract informative statistics.
tntorch is a PyTorch-powered library for tensor network modeling and learning. It supports tensor decomposition and mani-pulation, statistics and sensitivity metrics, classification, optimization (using auto-differentiation), and more. It includes numerous tutorials covering all featured use cases.