Related papers: Efficient computational homogenization via tensor …
Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…
Many-body correlations in strongly coupled liquids and plasmas are critical for many applications in nanofluids, biology, and fusion-related plasma physics, but their description in fully heterogeneous environments remains challenging due…
Structural reliability evaluation for composites constitutes a fundamentally high-dimensional multiscale problem, as microscale material uncertainties must propagate to the macroscale and can be quantified as high-dimensional random fields.…
We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…
The effective large-scale properties of materials with random heterogeneities on a small scale are typically determined by the method of representative volumes: A sample of the random material is chosen - the representative volume - and its…
This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. Firstly, the second-order two-scale (SOTS) solutions for these…
Machine learning (ML) can facilitate efficient thermoelectric (TE) material discovery essential to address the environmental crisis. However, ML models often suffer from poor experimental generalizability despite high metrics. This study…
Atomic scale simulations are a key element of modern science in that they allow to understand, and even predict, complex physical or chemical phenomena on the basis of the fundamental laws of nature. Among the different existing atomic…
Bayesian inference in high-dimensional discrete-input additive noise models is a fundamental challenge in communication systems, as the support of the required joint a posteriori probability (APP) mass function grows exponentially with the…
Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…
Tensor Train~(TT) decomposition is widely used in the machine learning and quantum physics communities as a popular tool to efficiently compress high-dimensional tensor data. In this paper, we propose an efficient algorithm to accelerate…
In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…
The investigation of quantum impurity models plays a crucial role in condensed matter physics because of their wide-ranging applications, such as embedding theories and transport problems. Traditional methods often fall short of producing…
In our previous papers we have described efficient and reliable methods of generation of representative volume elements (RVE) perfectly suitable for analysis of composite materials via stochastic homogenization. In this paper we profit from…
Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
In this article, we design an original solver based on Quantized Tensor Trains (QTT) for linear elliptic equations with heterogeneous coefficient field, that allows for extremely fine meshes. It can achieve full-field simulations in…
Understanding and predicting thermal transport in disordered materials remains a significant challenge due to the absence of periodicity and the complex nature of medium-range structural motifs. In this work, we investigate amorphous…
There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…
Thermal conductivity of hadron matter is studied using a microscopic transport model, which will be used to simulate ultra-relativistic heavy ion collisions at different energy densities, namely the Ultra-relativistic Quantum Molecular…