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Related publications (22)

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COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

Laura Grigori

Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine ...

Siam Publications2024

Rank-Adaptive Time Integration Of Tree Tensor Networks

Gianluca Ceruti

A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves to the root, the integrator updates bases and then evolves connection tenso ...

SIAM PUBLICATIONS2023

STREAMING TENSOR TRAIN APPROXIMATION

Daniel Kressner

Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the streaming tensor train approximation (STTA), a new class of algorithms for approximating a given tensor ' in the tensor train fo ...

Siam Publications2023

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

Alfio Quarteroni, Francesco Regazzoni

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

Elsevier Science Sa2023

Mutual information for low-rank even-order symmetric tensor estimation

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method orig ...

Oxford University Press2021

Locally supported tangential vector, n-vector, and tensor fields

Christopher Brandt

We introduce a construction of subspaces of the spaces of tangential vector, n-vector, and tensor fields on surfaces. The resulting subspaces can be used as the basis of fast approximation algorithms for design and processing problems that involve tangenti ...

2020

Complements to Mugge and Friedel's Theory of Twinning

Cyril Cayron

The crystallography of twinning is based on the concepts of simple shear and obliquity introduced by Mugge, Mallard and Friedel at the turn of the last century, with tensor mathematics later developed by Bilby, Bevis and Crocker in the 1960s. We propose a ...

2020

Tensor Robust Pca On Graphs

Pierre Vandergheynst, Nauman Shahid, Francesco Grassi

We propose a graph signal processing framework to overcome the computational burden of Tensor Robust PCA (TRPCA). Our framework also serves as a convex alternative to graph regularized tensor factorization methods. Our method is based on projecting a tenso ...

IEEE2019

Mutual Information for Low-Rank Even-Order Symmetric Tensor Factorization

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its mutual information when the tensor is of even order. The proof uses the adaptive interpolation method, for which rank-on ...

IEEE2019

A comprehensive framework for visual quality assessment of light field tensor displays

Touradj Ebrahimi, Irene Viola

In recent years, light field technology has attracted the interest of academia and industry, thanks to the possibility of rendering 3D scenes in a more realistic and immersive way. In particular, light field displays have been consistently investigated for ...

Society for Imaging Science and Technology2019

Penalization and Bayesian numerical methods for multiscale inverse problems

Andrea Di Blasio

In this thesis we consider inverse problems involving multiscale elliptic partial differential equations. The name multiscale indicates that these models are characterized by the presence of parameters which vary on different spatial scales (macroscopic, m ...

EPFL2019

Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic

Mikko Tapani Korhonen

Let

G

be a classical group with natural module

V

over an algebraically closed field of good characteristic. For every unipotent element

u

G

, we describe the Jordan block sizes of

u

on the irreducible

G

-modules which occur as compositio ...

American Mathematical Society (AMS)2019

3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data

Mario Geiger

We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equiva ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Multilinear Low-Rank Tensors on Graphs & Applications

Pierre Vandergheynst, Nauman Shahid, Francesco Grassi

We propose a new framework for the analysis of low- rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank S ...

2016

Charge transport in superionic and melted AgI under a magnetic field studied via molecular dynamics

Sara Bonella

Charge transport in AgI subject to an external magnetic field is studied via computer simulations. We demonstrate that a recently developed algorithm can effectively complement problematic experiments to detect the ionic Hall effect, and identify previousl ...

Amer Physical Soc2016

Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Assyr Abdulle, Timothée Noé Pouchon

A family of effective equations that capture the long time dispersive effects of wave propagation in heterogeneous media in an arbitrary large periodic spatial domain Omega subset of R-d is proposed and analyzed. For a wave equation with highly oscillatory ...

World Scientific Publ Co Pte Ltd2016

Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Daniel Kressner, Fabio Nobile, Christine Tobler, Rajesh Kumar

Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochas ...

2015

Learning with tensors: a framework based on convex optimization and spectral regularization

Quoc Tran Dinh

We present a framework based on convex optimization and spectral regularization to perform learning when feature observations are multidimensional arrays (tensors). We give a mathematical characterization of spectral penalties for tensors and analyze a uni ...

Springer2014

Dynamical Approximation By Hierarchical Tucker And Tensor-Train Tensors

We extend results on the dynamical low-rank approximation for the treatment of time-dependent matrices and tensors (Koch and Lubich; see [SIAM J. Matrix Anal. Appl., 29 (2007), pp. 434-454], [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2360-2375]) to the re ...

Society for Industrial and Applied Mathematics2013

Light Field Tensor Recovery

Pierre Vandergheynst, Mahdad Hosseini Kamal

This paper presents a novel approach to capture light field in camera arrays based on the tensor recovery framework. Light fields are acquired by a linear array of cameras with overlapping field of view. We represent the light fields in shape of a tensor t ...

2012