Low-rank tensor representations can provide highly compressed approximations of
functions. These concepts, which essentially amount to generalizations of classical …

Part 2 of this monograph builds on the introduction to tensor networks and their operations
presented in Part 1. It focuses on tensor network models for super-compressed higher-order …

Modern applications in engineering and data science are increasingly based on
multidimensional data of exceedingly high volume, variety, and structural richness …

Tensor networks have in recent years emerged as the powerful tools for solving the large-
scale optimization problems. One of the most popular tensor network is tensor train (TT) …

The curse of dimensionality associated with the Hilbert space of spin systems provides a
significant obstruction to the study of condensed matter systems. Tensor networks have …

During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …

We propose an improved scheme to do the time-dependent variational principle (TDVP) in
finite matrix product states (MPSs) for two-dimensional systems or one-dimensional systems …

In recent years, low-rank based tensor completion, which is a higher order extension of
matrix completion, has received considerable attention. However, the low-rank assumption …

In various engineering and applied science applications, repetitive numerical simulations of
partial differential equations (PDEs) for varying input parameters are often required (eg …

Many problems in computational neuroscience, neuroinformatics, pattern/image recognition,
signal processing and machine learning generate massive amounts of multidimensional …