We developed a new method PROTES for black-box optimization, which is based on the
probabilistic sampling from a probability density function given in the low-parametric tensor …

Tensor network techniques, known for their low-rank approximation ability that breaks the
curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra …

In this paper, we introduce a high-order tensor-train (TT) finite volume method for the
Shallow Water Equations (SWEs). We present the implementation of the $3^{rd} $ order …

Tensor network techniques, known for their low-rank approximation ability that breaks the
curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra …

This work explores the representation of univariate and multivariate functions as matrix
product states (MPS), also known as quantized tensor-trains (QTT). It proposes an algorithm …

We propose a tensor train based data structure to accelerate the calculation of Dempster-
Shafer operations such as belief and Dempster's rule of combination. This approach relies …

Originally, low-rank tensor decomposition algorithms were designed to approximate high-
dimensional tensors. Due to its mathematical characteristics, Tensor-Train decomposition, a …

We propose a tensor train based data structure to accelerate the calculation of Dempster-
Shafer operations such as belief and Dempster's rule of combination. This approach relies …