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An Additive Two-Level Parallel Variant of the DMRG Algorithm with Coarse-Space Correction.

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Title: An Additive Two-Level Parallel Variant of the DMRG Algorithm with Coarse-Space Correction.
Authors: Grigori, Laura1 (AUTHOR) laura.grigori@epfl.ch, Hassan, Muhammad2 (AUTHOR) muhammad.hassan@psi.ch
Source: SIAM Journal on Scientific Computing. 2026, Vol. 48 Issue 3, pA1312-A1337. 26p.
Subjects: Domain decomposition methods, Optimization algorithms, Parallel programming, Mathematical optimization, Chemical 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. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 195222019
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Scientific+Computing%22">SIAM Journal on Scientific Computing</searchLink>. 2026, Vol. 48 Issue 3, pA1312-A1337. 26p.
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  Data: <searchLink fieldCode="DE" term="%22Domain+decomposition+methods%22">Domain decomposition methods</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Parallel+programming%22">Parallel programming</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Chemical+systems%22">Chemical systems</searchLink>
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Group: Ab
  Data: <i>Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1137/25M1764487
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 26
        StartPage: A1312
    Subjects:
      – SubjectFull: Domain decomposition methods
        Type: general
      – SubjectFull: Optimization algorithms
        Type: general
      – SubjectFull: Parallel programming
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Chemical systems
        Type: general
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      – TitleFull: An Additive Two-Level Parallel Variant of the DMRG Algorithm with Coarse-Space Correction.
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            NameFull: Grigori, Laura
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            NameFull: Hassan, Muhammad
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              Text: 2026
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              Y: 2026
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              Value: 48
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            – TitleFull: SIAM Journal on Scientific Computing
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