Related papers: Extended tensor decomposition model reduction meth…

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…

Temporal difference (TD) methods constitute a class of methods for learning predictions in multi-step prediction problems, parameterized by a recency factor lambda. Currently the most important application of these methods is to temporal…

Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…

Tensor decomposition has recently been gaining attention in the machine learning community for the analysis of individual traces, such as Electronic Health Records (EHR). However, this task becomes significantly more difficult when the data…

Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…

Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand…

The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…

Tensor decompositions are powerful tools for dimensionality reduction and feature interpretation of multidimensional data such as signals. Existing tensor decomposition objectives (e.g., Frobenius norm) are designed for fitting raw data…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

The study is devoted to geometrically non-linear modelling of viscoplastic structures with residual stresses. We advocate and develop a special approach to residual stresses based on the transition between reference configurations. The…

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) decomposition that acts as the building blocks for the…

A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current…

Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…

Singular value decomposition (SVD) is one of the most popular compression methods that approximate a target matrix with smaller matrices. However, standard SVD treats the parameters within the matrix with equal importance, which is a simple…

We propose a non-intrusive, Autoencoder-based framework for reduced-order modeling in continuum mechanics. Our method integrates three stages: (i) an unsupervised Autoencoder compresses high-dimensional finite element solutions into a…

The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…

This paper offers an approach to deal with parametrized nonlinear strongly coupled thermo-poroelasticity problems. The approach uses the LATIN-PGD method and extends previous work in multiphysics problems. Proper Generalized Decomposition…

Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter…

Robust tensor principal component analysis (RTPCA) aims to separate the low-rank and sparse components from multi-dimensional data, making it an essential technique in the signal processing and computer vision fields. Recently emerging…

This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…