Efficient Construction of Canonical Polyadic Approximations of Tensor Networks

Pierce, Karl; Valeev, Edward F.

doi:10.1021/acs.jctc.2c00861

Efficient Construction of Canonical Polyadic Approximations of Tensor Networks

Journal Article · 09 December 2022 · Journal of Chemical Theory and Computation

DOI:https://doi.org/10.1021/acs.jctc.2c00861· OSTI ID:2422121

Pierce, Karl ^[1]; ^[2]

Department of Chemistry, Virginia Tech, Blacksburg, Virginia24061, United States; OSTI
Department of Chemistry, Virginia Tech, Blacksburg, Virginia24061, United States

Not provided.

Research Organization:: Florida State Univ., Tallahassee, FL (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0022263

OSTI ID:: 2422121

Journal Information:: Journal of Chemical Theory and Computation, Journal Name: Journal of Chemical Theory and Computation Journal Issue: 1 Vol. 19; ISSN 1549-9618

Publisher:: American Chemical Society

Country of Publication:: United States

Language:: English

References (68)

Principal component analysis of three-mode data by means of alternating least squares algorithms Kroonenberg, Pieter M.; de Leeuw, Jan Psychometrika, Vol. 45, Issue 1 https://doi.org/10.1007/BF02293599	journal	March 1980
A scalable optimization approach for fitting canonical tensor decompositions Acar, Evrim; Dunlavy, Daniel M.; Kolda, Tamara G. Journal of Chemometrics, Vol. 25, Issue 2 https://doi.org/10.1002/cem.1335	journal	January 2011
Pseudospectral multireference single and double excitation configuration interaction Martinez, Todd J.; Carter, Emily A. The Journal of Chemical Physics, Vol. 102, Issue 19 https://doi.org/10.1063/1.469088	journal	May 1995
Fast adaptive algorithms in the non-standard form for multidimensional problems Beylkin, Gregory; Cheruvu, Vani; Pérez, Fernando Applied and Computational Harmonic Analysis, Vol. 24, Issue 3 https://doi.org/10.1016/j.acha.2007.08.001	journal	May 2008
Tensor Decompositions and Applications Kolda, Tamara G.; Bader, Brett W. SIAM Review, Vol. 51, Issue 3 https://doi.org/10.1137/07070111X	journal	August 2009
Rank reduced coupled cluster theory. I. Ground state energies and wavefunctions Parrish, Robert M.; Zhao, Yao; Hohenstein, Edward G. The Journal of Chemical Physics, Vol. 150, Issue 16 https://doi.org/10.1063/1.5092505	journal	April 2019
Low Complexity Damped Gauss--Newton Algorithms for CANDECOMP/PARAFAC Phan, Anh-Huy; Tichavský, Petr; Cichocki, Andrzej SIAM Journal on Matrix Analysis and Applications, Vol. 34, Issue 1 https://doi.org/10.1137/100808034	journal	January 2013
Auxiliary basis expansions for large-scale electronic structure calculations Jung, Y.; Sodt, A.; Gill, P. M. W. Proceedings of the National Academy of Sciences, Vol. 102, Issue 19 https://doi.org/10.1073/pnas.0408475102	journal	April 2005
Tensor rank is NP-complete Håstad, Johan Journal of Algorithms, Vol. 11, Issue 4 https://doi.org/10.1016/0196-6774(90)90014-6	journal	December 1990
New Methods For Electronic Structure Calculations on Large Molecules Friesner, R. A. Annual Review of Physical Chemistry, Vol. 42, Issue 1 https://doi.org/10.1146/annurev.pc.42.100191.002013	journal	October 1991
Integral approximations for LCAO-SCF calculations Vahtras, O.; Almlöf, J.; Feyereisen, M. W. Chemical Physics Letters, Vol. 213, Issue 5-6 https://doi.org/10.1016/0009-2614(93)89151-7	journal	October 1993
Numerical operator calculus in higher dimensions Beylkin, G.; Mohlenkamp, M. J. Proceedings of the National Academy of Sciences, Vol. 99, Issue 16 https://doi.org/10.1073/pnas.112329799	journal	July 2002
Tensor hypercontraction. II. Least-squares renormalization Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J. The Journal of Chemical Physics, Vol. 137, Issue 22 https://doi.org/10.1063/1.4768233	journal	December 2012
Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory Hohenstein, Edward G.; Parrish, Robert M.; Martínez, Todd J. The Journal of Chemical Physics, Vol. 137, Issue 4 https://doi.org/10.1063/1.4732310	journal	July 2012
Coulombic potential energy integrals and approximations Whitten, J. L. The Journal of Chemical Physics, Vol. 58, Issue 10 https://doi.org/10.1063/1.1679012	journal	May 1973
Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange Neese, Frank; Wennmohs, Frank; Hansen, Andreas Chemical Physics, Vol. 356, Issue 1-3 https://doi.org/10.1016/j.chemphys.2008.10.036	journal	February 2009
Topographic components model for event-related potentials and some biophysical considerations Mocks, J. IEEE Transactions on Biomedical Engineering, Vol. 35, Issue 6 https://doi.org/10.1109/10.2119	journal	June 1988
The impact of the resolution of the identity approximate integral method on modern ab initio algorithm development Kendall, Rick A.; Früchtl, Herbert A. Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 97, Issue 1-4 https://doi.org/10.1007/s002140050249	journal	October 1997
A fast algorithm for particle simulations Greengard, L.; Rokhlin, V. Journal of Computational Physics, Vol. 73, Issue 2 https://doi.org/10.1016/0021-9991(87)90140-9	journal	December 1987
A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format Espig, Mike; Hackbusch, Wolfgang Numerische Mathematik, Vol. 122, Issue 3 https://doi.org/10.1007/s00211-012-0465-9	journal	May 2012
Ab initioanalytical molecular gradients and Hessians Jo/rgensen, Poul; Simons, Jack The Journal of Chemical Physics, Vol. 79, Issue 1 https://doi.org/10.1063/1.445528	journal	July 1983
Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition Carroll, J. Douglas; Chang, Jih-Jie Psychometrika, Vol. 35, Issue 3 https://doi.org/10.1007/BF02310791	journal	September 1970
Some properties of inner projections Löwdin, Per-Olov International Journal of Quantum Chemistry, Vol. 5, Issue S4 https://doi.org/10.1002/qua.560050725	journal	January 1970
Reliably assessing the electronic structure of cytochrome P450 on today’s classical computers and tomorrow’s quantum computers Goings, Joshua J.; White, Alec; Lee, Joonho Proceedings of the National Academy of Sciences, Vol. 119, Issue 38 https://doi.org/10.1073/pnas.2203533119	journal	September 2022
Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory Lee, Joonho; Lin, Lin; Head-Gordon, Martin Journal of Chemical Theory and Computation, Vol. 16, Issue 1 https://doi.org/10.1021/acs.jctc.9b00820	journal	November 2019
Tensor product approximation with optimal rank in quantum chemistry Chinnamsetty, Sambasiva Rao; Espig, Mike; Khoromskij, Boris N. The Journal of Chemical Physics, Vol. 127, Issue 8 https://doi.org/10.1063/1.2761871	journal	August 2007
Low-order tensor approximations for electronic wave functions: Hartree–Fock method with guaranteed precision Bischoff, Florian A.; Valeev, Edward F. The Journal of Chemical Physics, Vol. 134, Issue 10 https://doi.org/10.1063/1.3560091	journal	March 2011
Accelerating alternating least squares for tensor decomposition by pairwise perturbation Ma, Linjian; Solomonik, Edgar Numerical Linear Algebra with Applications, Vol. 29, Issue 4 https://doi.org/10.1002/nla.2431	journal	January 2022
The Expression of a Tensor or a Polyadic as a Sum of Products Hitchcock, Frank L. Journal of Mathematics and Physics, Vol. 6, Issue 1-4 https://doi.org/10.1002/sapm192761164	journal	April 1927
Solution of self-consistent field electronic structure equations by a pseudospectral method Friesner, Richard A. Chemical Physics Letters, Vol. 116, Issue 1 https://doi.org/10.1016/0009-2614(85)80121-4	journal	April 1985
Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2 Hohenstein, Edward G.; Kokkila, Sara I. L.; Parrish, Robert M. The Journal of Chemical Physics, Vol. 138, Issue 12 https://doi.org/10.1063/1.4795514	journal	March 2013
Pseudospectral Hartree–Fock theory: Applications and algorithmic improvements Ringnalda, Murco N.; Belhadj, Mahfoud; Friesner, Richard A. The Journal of Chemical Physics, Vol. 93, Issue 5 https://doi.org/10.1063/1.458819	journal	September 1990
Simplifications in the generation and transformation of two-electron integrals in molecular calculations Beebe, Nelson H. F.; Linderberg, Jan International Journal of Quantum Chemistry, Vol. 12, Issue 4 https://doi.org/10.1002/qua.560120408	journal	October 1977
Most Tensor Problems Are NP-Hard Hillar, Christopher J.; Lim, Lek-Heng Journal of the ACM, Vol. 60, Issue 6 https://doi.org/10.1145/2512329	journal	November 2013
Pseudospectral generalized valence‐bond calculations: Application to methylene, ethylene, and silylene Langlois, Jean‐Marc; Muller, Richard P.; Coley, Terry R. The Journal of Chemical Physics, Vol. 92, Issue 12 https://doi.org/10.1063/1.458184	journal	June 1990
Quantum Chemical Benchmark Energy and Geometry Database for Molecular Clusters and Complex Molecular Systems (www.begdb.com): A Users Manual and Examples Řezáč, Jan; Jurečka, Petr; Riley, Kevin E. Collection of Czechoslovak Chemical Communications, Vol. 73, Issue 10 https://doi.org/10.1135/cccc20081261	journal	January 2008
Pseudospectral full configuration interaction Martinez, Todd J.; Mehta, Aseem; Carter, Emily A. The Journal of Chemical Physics, Vol. 97, Issue 3 https://doi.org/10.1063/1.463176	journal	August 1992
Tensor decomposition in post-Hartree–Fock methods. I. Two-electron integrals and MP2 Benedikt, Udo; Auer, Alexander A.; Espig, Mike The Journal of Chemical Physics, Vol. 134, Issue 5 https://doi.org/10.1063/1.3514201	journal	February 2011
Studies in Perturbation Theory. IX. Connection Between Various Approaches in the Recent Development—Evaluation of Upper Bounds to Energy Eigenvalues in Schrödinger's Perturbation Theory Löwdin, Per-Olov Journal of Mathematical Physics, Vol. 6, Issue 8 https://doi.org/10.1063/1.1704781	journal	August 1965
Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations with Applications to Defects in Silicon Hu, Wei; Lin, Lin; Yang, Chao Journal of Chemical Theory and Computation, Vol. 13, Issue 11 https://doi.org/10.1021/acs.jctc.7b00807	journal	October 2017
Pseudospectral time-dependent density functional theory Ko, Chaehyuk; Malick, David K.; Braden, Dale A. The Journal of Chemical Physics, Vol. 128, Issue 10 https://doi.org/10.1063/1.2834222	journal	March 2008
Systematically convergent basis sets for explicitly correlated wavefunctions: The atoms H, He, B–Ne, and Al–Ar Peterson, Kirk A.; Adler, Thomas B.; Werner, Hans-Joachim The Journal of Chemical Physics, Vol. 128, Issue 8 https://doi.org/10.1063/1.2831537	journal	February 2008
Parallel algorithms for tensor completion in the CP format Karlsson, Lars; Kressner, Daniel; Uschmajew, André Parallel Computing, Vol. 57 https://doi.org/10.1016/j.parco.2015.10.002	journal	September 2016
Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations Weigend, Florian; Köhn, Andreas; Hättig, Christof The Journal of Chemical Physics, Vol. 116, Issue 8 https://doi.org/10.1063/1.1445115	journal	February 2002
Tensor representation techniques for full configuration interaction: A Fock space approach using the canonical product format Böhm, Karl-Heinz; Auer, Alexander A.; Espig, Mike The Journal of Chemical Physics, Vol. 144, Issue 24 https://doi.org/10.1063/1.4953665	journal	June 2016
Robust Approximation of Tensor Networks: Application to Grid-Free Tensor Factorization of the Coulomb Interaction Pierce, Karl; Rishi, Varun; Valeev, Edward F. Journal of Chemical Theory and Computation, Vol. 17, Issue 4 https://doi.org/10.1021/acs.jctc.0c01310	journal	March 2021
S66: A Well-balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures Řezáč, Jan; Riley, Kevin E.; Hobza, Pavel Journal of Chemical Theory and Computation, Vol. 7, Issue 8 https://doi.org/10.1021/ct2002946	journal	July 2011
Structure of the Hessian matrix and an economical implementation of Newton’s method in the problem of canonical approximation of tensors Kazeev, V. A.; Tyrtyshnikov, E. E. Computational Mathematics and Mathematical Physics, Vol. 50, Issue 6 https://doi.org/10.1134/S0965542510060011	journal	June 2010
Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction Parrish, Robert M.; Sherrill, C. David; Hohenstein, Edward G. The Journal of Chemical Physics, Vol. 140, Issue 18 https://doi.org/10.1063/1.4876016	journal	May 2014
An efficient algorithm for Cholesky decomposition of electron repulsion integrals Folkestad, Sarai D.; Kjønstad, Eirik F.; Koch, Henrik The Journal of Chemical Physics, Vol. 150, Issue 19 https://doi.org/10.1063/1.5083802	journal	May 2019
Towards a standardized notation and terminology in multiway analysis Kiers, Henk A. L. Journal of Chemometrics, Vol. 14, Issue 3 https://doi.org/10.1002/1099-128X(200005/06)14:3<105::AID-CEM582>3.0.CO;2-I	journal	January 2000
Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations Peng, Bo; Kowalski, Karol Journal of Chemical Theory and Computation, Vol. 13, Issue 9 https://doi.org/10.1021/acs.jctc.7b00605	journal	August 2017
Variational calculus with sums of elementary tensors of fixed rank Espig, Mike; Hackbusch, Wolfgang; Rohwedder, Thorsten Numerische Mathematik, Vol. 122, Issue 3 https://doi.org/10.1007/s00211-012-0464-x	journal	May 2012
Tensor decomposition in post-Hartree–Fock methods. II. CCD implementation Benedikt, Udo; Böhm, Karl-Heinz; Auer, Alexander A. The Journal of Chemical Physics, Vol. 139, Issue 22 https://doi.org/10.1063/1.4833565	journal	December 2013
A Practical Randomized CP Tensor Decomposition Battaglino, Casey; Ballard, Grey; Kolda, Tamara G. SIAM Journal on Matrix Analysis and Applications, Vol. 39, Issue 2 https://doi.org/10.1137/17M1112303	journal	January 2018
On first-row diatomic molecules and local density models Dunlap, B. I.; Connolly, J. W. D.; Sabin, J. R. The Journal of Chemical Physics, Vol. 71, Issue 12 https://doi.org/10.1063/1.438313	journal	January 1979
Tensor-structured coupled cluster theory Schutski, Roman; Zhao, Jinmo; Henderson, Thomas M. The Journal of Chemical Physics, Vol. 147, Issue 18 https://doi.org/10.1063/1.4996988	journal	November 2017
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen Dunning, Thom H. The Journal of Chemical Physics, Vol. 90, Issue 2 https://doi.org/10.1063/1.456153	journal	January 1989
Low rank factorization of the Coulomb integrals for periodic coupled cluster theory Hummel, Felix; Tsatsoulis, Theodoros; Grüneis, Andreas The Journal of Chemical Physics, Vol. 146, Issue 12 https://doi.org/10.1063/1.4977994	journal	March 2017
Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost Lu, Jianfeng; Ying, Lexing Journal of Computational Physics, Vol. 302 https://doi.org/10.1016/j.jcp.2015.09.014	journal	December 2015
Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions Hohenstein, Edward G.; Parrish, Robert M.; Sherrill, C. David The Journal of Chemical Physics, Vol. 137, Issue 22 https://doi.org/10.1063/1.4768241	journal	December 2012
Pseudospectral Mo/ller–Plesset perturbation theory through third order Martinez, Todd J.; Carter, Emily A. The Journal of Chemical Physics, Vol. 100, Issue 5 https://doi.org/10.1063/1.466350	journal	March 1994
Global minima of water clusters (H2O)n, n≤21, described by an empirical potential Wales, David J.; Hodges, Matthew P. Chemical Physics Letters, Vol. 286, Issue 1-2 https://doi.org/10.1016/S0009-2614(98)00065-7	journal	April 1998
Optimization-Based Algorithms for Tensor Decompositions: Canonical Polyadic Decomposition, Decomposition in Rank-$(L_r,L_r,1)$ Terms, and a New Generalization Sorber, Laurent; Van Barel, Marc; De Lathauwer, Lieven SIAM Journal on Optimization, Vol. 23, Issue 2 https://doi.org/10.1137/120868323	journal	January 2013
Elimination of energy denominators in Møller—Plesset perturbation theory by a Laplace transform approach Almlöf, Jan Chemical Physics Letters, Vol. 181, Issue 4 https://doi.org/10.1016/0009-2614(91)80078-C	journal	June 1991
Pseudospectral double excitation configuration interaction Martinez, Todd J.; Carter, Emily A. The Journal of Chemical Physics, Vol. 98, Issue 9 https://doi.org/10.1063/1.464751	journal	May 1993
A further improvement of a fast damped Gauss-Newton algorithm for candecomp-parafac tensor decomposition Tichavsky, Petr; Phan, Anh Huy; Cichocki, Andrzej 2013 IEEE International Conference on Acoustics, Speech and Signal Processing https://doi.org/10.1109/ICASSP.2013.6638809	conference	May 2013
Solution of the Hartree–Fock equations by a pseudospectral method: Application to diatomic molecules Friesner, Richard A. The Journal of Chemical Physics, Vol. 85, Issue 3 https://doi.org/10.1063/1.451237	journal	August 1986

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