SIAM Journal on Numerical Analysis· 2015Q1
Time Integration of Tensor Trains
- 177citations
- Q1SCImago
- 2015year
Short summary
A new time integrator efficiently updates time-dependent tensors in the tensor train format, enabling approximate solutions to high-dimensional tensor differential equations.
AI-generated from the title and abstract; the full text is not read.
Key points
- Presents a novel time integrator for tensor train/matrix product state formats.
- The method is based on splitting the projector onto the tangent space of the tensor manifold.
- Enables updating time-dependent tensors and solving high-dimensional tensor differential equations.
- Validated through numerical experiments in quantum molecular dynamics and iterative tensor train processes.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. SIAM Journal on Numerical Analysis, 2015 · DOI ↗
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Field: Computational Mathematics
Computational MathematicsMathematics