An additive two-level parallel variant of the DMRG algorithm with coarse-space correction

TL;DR

This paper introduces an additive two-level parallel DMRG algorithm that enhances scalability and efficiency for high-dimensional tensor problems by combining local and global minimization steps suitable for distributed computing.

Contribution

The paper presents a novel additive two-level DMRG algorithm inspired by Schwarz methods, enabling parallel implementation and improved convergence for tensor train problems.

Findings

Achieves competitive convergence rates.

Provides significant parallel speedups.

Effective for strongly correlated molecular systems.

Abstract

The density matrix renormalization group (DMRG) algorithm is a popular alternating minimization scheme for solving high-dimensional optimization problems in the tensor train format. Classical DMRG, however, is based on sequential minimization, which raises challenges in its implementation on parallel computing architectures. To overcome this, we propose a novel additive two-level DMRG algorithm that combines independent, local minimization steps with a global update step using a subsequent coarse-space minimization. Our proposed algorithm, which is directly inspired by additive Schwarz methods from the domain decomposition literature, is particularly amenable to implementation on parallel, distributed architectures since both the local minimization steps and the construction of the coarse-space can be performed in parallel. Numerical experiments on strongly correlated molecular systems demonstrate that the method achieves competitive convergence rates while achieving significant parallel speedups.