Automated operation minimization of tensor contraction expressions in electronic structure calculations

Albert Hartono; Alexander Sibiryakov; Marcel Nooijen; Gerald Baumgartner; David E. Bernholdt; So Hirata; Chi Chung Lam; Russell M. Pitzer; J. Ramanujam; P. Sadayappan

doi:10.1007/11428831_20

Automated operation minimization of tensor contraction expressions in electronic structure calculations

Albert Hartono, Alexander Sibiryakov, Marcel Nooijen, Gerald Baumgartner, David E. Bernholdt, So Hirata, Chi Chung Lam, Russell M. Pitzer, J. Ramanujam, P. Sadayappan

Research output: Contribution to journal › Conference article › peer-review

24 Scopus citations

Abstract

Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the Coupled Cluster method. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions, but the optimization problem is NP-hard. Operation minimization is an important optimization step for the Tensor Contraction Engine, a tool being developed for the automatic transformation of high-level tensor contraction expressions into efficient programs. In this paper, we develop an effective heuristic approach to the operation minimization problem, and demonstrate its effectiveness on tensor contraction expressions for coupled cluster equations.

Original language	English
Pages (from-to)	155-164
Number of pages	10
Journal	Lecture Notes in Computer Science
Volume	3514
Issue number	I
DOIs	https://doi.org/10.1007/11428831_20
State	Published - 2005
Event	5th International Conference on Computational Science - ICCS 2005 - Atlanta, GA, United States Duration: May 22 2005 → May 25 2005

Funding

Acknowledgments. This work has been supported in part by the U.S. National Science Foundation, the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory (ORNL), and by a Discovery grant from the Natural Sciences and Engineering Research Council of Canada. ORNL is managed by UT-Battelle, LLC for the US Dept. of Energy under contract DE-AC-05-00OR22725.

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title = "Automated operation minimization of tensor contraction expressions in electronic structure calculations",

abstract = "Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the Coupled Cluster method. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions, but the optimization problem is NP-hard. Operation minimization is an important optimization step for the Tensor Contraction Engine, a tool being developed for the automatic transformation of high-level tensor contraction expressions into efficient programs. In this paper, we develop an effective heuristic approach to the operation minimization problem, and demonstrate its effectiveness on tensor contraction expressions for coupled cluster equations.",

author = "Albert Hartono and Alexander Sibiryakov and Marcel Nooijen and Gerald Baumgartner and Bernholdt, {David E.} and So Hirata and Lam, {Chi Chung} and Pitzer, {Russell M.} and J. Ramanujam and P. Sadayappan",

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language = "English",

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pages = "155--164",

journal = "Lecture Notes in Computer Science",

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note = "5th International Conference on Computational Science - ICCS 2005 ; Conference date: 22-05-2005 Through 25-05-2005",

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TY - JOUR

T1 - Automated operation minimization of tensor contraction expressions in electronic structure calculations

AU - Hartono, Albert

AU - Sibiryakov, Alexander

AU - Nooijen, Marcel

AU - Baumgartner, Gerald

AU - Bernholdt, David E.

AU - Hirata, So

AU - Lam, Chi Chung

AU - Pitzer, Russell M.

AU - Ramanujam, J.

AU - Sadayappan, P.

PY - 2005

Y1 - 2005

N2 - Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the Coupled Cluster method. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions, but the optimization problem is NP-hard. Operation minimization is an important optimization step for the Tensor Contraction Engine, a tool being developed for the automatic transformation of high-level tensor contraction expressions into efficient programs. In this paper, we develop an effective heuristic approach to the operation minimization problem, and demonstrate its effectiveness on tensor contraction expressions for coupled cluster equations.

AB - Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the Coupled Cluster method. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions, but the optimization problem is NP-hard. Operation minimization is an important optimization step for the Tensor Contraction Engine, a tool being developed for the automatic transformation of high-level tensor contraction expressions into efficient programs. In this paper, we develop an effective heuristic approach to the operation minimization problem, and demonstrate its effectiveness on tensor contraction expressions for coupled cluster equations.

UR - http://www.scopus.com/inward/record.url?scp=25144460585&partnerID=8YFLogxK

U2 - 10.1007/11428831_20

DO - 10.1007/11428831_20

M3 - Conference article

AN - SCOPUS:25144460585

SN - 0302-9743

VL - 3514

SP - 155

EP - 164

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

IS - I

T2 - 5th International Conference on Computational Science - ICCS 2005

Y2 - 22 May 2005 through 25 May 2005

ER -

Automated operation minimization of tensor contraction expressions in electronic structure calculations

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