Tensor networks for dimensionality reduction and large-scale optimization: Part 1 low-rank tensor decompositions

A Cichocki, N Lee, I Oseledets, AH Phan… - … and Trends® in …, 2016 - nowpublishers.com
Modern applications in engineering and data science are increasingly based on
multidimensional data of exceedingly high volume, variety, and structural richness …

Low-rank tensor networks for dimensionality reduction and large-scale optimization problems: Perspectives and challenges part 1

A Cichocki, N Lee, IV Oseledets, AH Phan… - arXiv preprint arXiv …, 2016 - arxiv.org
Machine learning and data mining algorithms are becoming increasingly important in
analyzing large volume, multi-relational and multi--modal datasets, which are often …

Cross tensor approximation methods for compression and dimensionality reduction

S Ahmadi-Asl, CF Caiafa, A Cichocki, AH Phan… - IEEE …, 2021 - ieeexplore.ieee.org
Cross Tensor Approximation (CTA) is a generalization of Cross/skeleton matrix and CUR
Matrix Approximation (CMA) and is a suitable tool for fast low-rank tensor approximation. It …

Physics-informed machine learning combining experiment and simulation for the design of neodymium-iron-boron permanent magnets with reduced critical-elements …

A Kovacs, J Fischbacher, H Oezelt, A Kornell… - Frontiers in …, 2023 - frontiersin.org
Rare-earth elements like neodymium, terbium and dysprosium are crucial to the
performance of permanent magnets used in various green-energy technologies like hybrid …

A comparison of zonotope order reduction techniques

X Yang, JK Scott - Automatica, 2018 - Elsevier
This brief paper provides a comparison of methods for enclosing a given zonotope within
another of lower complexity, commonly called order reduction. These techniques are …

Evaluation of Docking Target Functions by the Comprehensive Investigation of Protein‐Ligand Energy Minima

IV Oferkin, EV Katkova, AV Sulimov… - Advances in …, 2015 - Wiley Online Library
The adequate choice of the docking target function impacts the accuracy of the ligand
positioning as well as the accuracy of the protein‐ligand binding energy calculation. To …

An Exponential Time Integrator for the Incompressible Navier--Stokes Equation

GL Kooij, MA Botchev, BJ Geurts - SIAM journal on scientific computing, 2018 - SIAM
We present an exponential time integration method for the incompressible Navier--Stokes
equation. An essential step in our procedure is the treatment of the pressure by applying a …

Accuracy comparison of several common implicit solvent models and their implementations in the context of protein-ligand binding

EV Katkova, AV Onufriev, B Aguilar… - Journal of Molecular …, 2017 - Elsevier
In this study several commonly used implicit solvent models are compared with respect to
their accuracy of estimating solvation energies of small molecules and proteins, as well as …

Efficient estimation for a smoothing thin plate spline in a two-dimensional space

J Cavieres, M Karkulik - arXiv preprint arXiv:2404.01902, 2024 - arxiv.org
Using a deterministic framework allows us to estimate a function with the purpose of
interpolating data in spatial statistics. Radial basis functions are commonly used for …

Supercomputer modelling of electromagnetic wave scattering with boundary integral equation method

A Aparinov, A Setukha, S Stavtsev - … –26, 2017, Revised Selected Papers 3, 2017 - Springer
Authors consider the approaches to increase efficiency of calculations in the problem of
numerical modelling of electromagnetic wave scattering. To solve such kind of problems …