TIME INTEGRATION OF TENSOR TRAINS
TIME INTEGRATION OF TENSOR TRAINS
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DOI：
10.1137/140976546
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发表时间：
2015-01-01
影响因子：
2.9
通讯作者：
Vandereycken, Bart
中科院分区：
文献类型：
--
作者：
Lubich, Christian;Oseledets, Ivan V.;Vandereycken, Bart
提出了一种稳健而有效的时间积分器，用于张量列或矩阵乘积状态格式的动态张量逼近。该方法基于将投影机分裂到张量流形的切线空间上。该算法可用于更新给定数据稀疏张量序列/矩阵乘积状态格式的含时张量，并可用于计算这种数据稀疏格式下的高维张量微分方程的近似解。对所提出的积分器的公式、实现和理论性质进行了研究，并对量子分子动力学问题和张量序列形式的迭代过程进行了数值实验。
A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train/matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formulation, implementation, and theoretical properties of the proposed integrator are studied, and numerical experiments with problems from quantum molecular dynamics and with iterative processes in the tensor train format are included.