Rank-Adaptive Time Integration of Tree Tensor Networks

DOI10.1137/22M1473790MaRDI QIDQ5886230

Gianluca Ceruti, Christian Lubich, Unnamed Author

Publication date: 31 March 2023

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.10291

zbMATH Keywords

dynamical low-rank approximationrank adaptivitytensor differential equationtree tensor network

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (5)

Low-rank tensor methods for partial differential equations ⋮ A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations ⋮ Accelerating the simulation of kinetic shear Alfvén waves with a dynamical low-rank approximation ⋮ Asymptotic-Preserving and Energy Stable Dynamical Low-Rank Approximation ⋮ A robust and conservative dynamical low-rank algorithm

Uses Software

• htucker

Cites Work

• Tensor Decompositions and Applications
• The geometry of algorithms using hierarchical tensors
• Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations
• The density-matrix renormalization group in the age of matrix product states
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• Geometry of the time-dependent variational principle in quantum mechanics
• Rank-adaptive tensor methods for high-dimensional nonlinear PDEs
• Tree-based tensor formats
• An unconventional robust integrator for dynamical low-rank approximation
• Time-evolution methods for matrix-product states
• A projector-splitting integrator for dynamical low-rank approximation
• Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values
• Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions
• Hierarchical Singular Value Decomposition of Tensors
• Time Integration in the Multiconfiguration Time-Dependent Hartree Method of Molecular Quantum Dynamics
• A Multilinear Singular Value Decomposition
• Time Integration of Rank-Constrained Tucker Tensors
• Time Integration of Tree Tensor Networks
• Algorithm 941
• Tensor Spaces and Numerical Tensor Calculus
• Time Integration of Tensor Trains

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