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مقاله‌ی دسترسی آزاد

Time Integration of Tree Tensor Networks

['Gianluca Ceruti', 'Christian Lubich', 'Hanna Walach', '']

چکیده

Dynamical low-rank approximation by tree tensor networks is studied for the data-sparse of large time-dependent data tensors and unknown solutions to differential equations. A time integration method prescribed rank presented analyzed. It extends known projector-splitting integrators dynamical matrices rank-constrained Tucker shown inherit their favorable properties. The integrator based on recursively applying integrator. In every step, climbs up down tree: it uses a recursion that passes from root leaves construction initial value problems subtree using appropriate restrictions prolongations, another update factors in network. reproduces given specified exactly robust typical presence small singular values matricizations connection tensors, contrast standard applied equations networks.

اسناد مشابه

  • Rank-Adaptive Time Integration of Tree Tensor Networks

    مقاله‌ی دسترسی آزاد۲۰۲۳SIAM Journal on Numerical Analysis['Gianluca Ceruti', 'Christian Lubich', 'Dominik Sulz', '']

    A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree networks is proposed and analyzed. In a recursion from leaves to root, updates bases then evolves connection tensors Galerkin method in augmented subspace spanned new old b

  • Tree Tensor Network State with Variable Tensor Order: An Efficient Multireference Method for Strongly Correlated Systems

    سند علمی۲۰۱۵Journal of chemical theory and computationV. Murg, F. Verstraete, R. Schneider, P. R. Nagy

    We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be consider

  • Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions

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    We study the approximation by tensor networks (TNs) of functions from classical smoothness classes. The considered tool combines a tensorization in $L^p([0,1))$, which allows to identify univariate function with multivariate (or tensor), and use tree (the train format) for exploi

  • Tree tensor-network real-time multiorbital impurity solver: Spin-orbit coupling and correlation functions in Sr 2 RuO 4

    مقاله‌ی دسترسی آزاد۲۰۲۱Physical Review B['Xian-An Cao', 'Ying Lu', 'Philipp Hansmann', 'Maurits W. Haverkort', '']

    We present a tree tensor-network impurity solver suited for general multiorbital systems. The network is constructed to efficiently capture the entanglement structure and symmetry of an problem. works directly on real-time/frequency axis generates spectral functions with energy-i

  • Entanglement bipartitioning and tree tensor networks

    مقاله‌ی دسترسی آزاد۲۰۲۳Progress of theoretical and experimental physics['Kouichi Okunishi', 'Hiroshi Ueda', 'Tomotoshi Nishino', '']

    We propose the entanglement bipartitioning approach to design an optimal network structure of tree-tensor-network (TTN) for quantum many-body systems. Given exact ground-state wavefunction, we perform sequential spin-cluster nodes so as minimize mutual information or maximum loss

  • Learning with tree tensor networks: Complexity estimates and model selection

    مقاله‌ی دسترسی آزاد۲۰۲۲Bernoulli['Bertrand Michel', 'Anthony Nouy', '']

    Tree tensor networks, or tree-based formats, are prominent model classes for the approximation of high-dimensional functions in computational and data science. They correspond to sum-product neural networks with a sparse connectivity associated dimension tree widths given by tupl