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Dynamical Approximation By Hierarchical Tucker And Tensor-Train Tensors

Related publications (31)

From low-rank retractions to dynamical low-rank approximation and back

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In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Springer2024

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

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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

STREAMING TENSOR TRAIN APPROXIMATION

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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

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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

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EPFL2023

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

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Elsevier Science Sa2023

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

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The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

EPFL2023

Critical Schrodinger Cat Qubit

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Encoding quantum information onto bosonic systems is a promising route to quantum error correc-tion. In a cat code, this encoding relies on the confinement of the dynamics of the system onto the two-dimensional manifold spanned by Schrodinger cats of oppos ...

AMER PHYSICAL SOC2023

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

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Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Dynamical Approximation By Hierarchical Tucker And Tensor-Train Tensors

From low-rank retractions to dynamical low-rank approximation and back

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

STREAMING TENSOR TRAIN APPROXIMATION

Rank-Adaptive Time Integration Of Tree Tensor Networks

Low-Rank Tensor Methods for High-Dimensional Problems

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

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Critical Schrodinger Cat Qubit

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Graph Chatbot

From low-rank retractions to dynamical low-rank approximation and back

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

STREAMING TENSOR TRAIN APPROXIMATION

Rank-Adaptive Time Integration Of Tree Tensor Networks

Low-Rank Tensor Methods for High-Dimensional Problems

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

Floyd's manifold is a conjugation space

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Critical Schrodinger Cat Qubit

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Floyd's manifold is a conjugation space