Cited by 120Advanced Chemical Physics StudiesMachine Learning in Materials ScienceComputational Drug Discovery Methods

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The many-body expansion combined with neural networks

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Yao, Kun, Herr, John E., Parkhill, John·2017·The Journal of Chemical Physics

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Abstract

Fragmentation methods such as the many-body expansion (MBE) are a common strategy to model large systems by partitioning energies into a hierarchy of decreasingly significant contributions. The number of calculations required for chemical accuracy is still prohibitively expensive for the ab initio MBE to compete with force field approximations for applications beyond single-point energies. Alongside the MBE, empirical models of ab initio potential energy surfaces have improved, especially non-linear models based on neural networks (NNs) which can reproduce ab initio potential energy surfaces rapidly and accurately. Although they are fast, NNs suffer from their own curse of dimensionality; they must be trained on a representative sample of chemical space. In this paper we examine the synergy of the MBE and NN’s and explore their complementarity. The MBE offers a systematic way to treat systems of arbitrary size while reducing the scaling problem of large systems. NN’s reduce, by a factor in excess of 106, the computational overhead of the MBE and reproduce the accuracy of ab initio calculations without specialized force fields. We show that for a small molecule extended system like methanol, accuracy can be achieved with drastically different chemical embeddings. To assess this we test a new chemical embedding which can be inverted to predict molecules with desired properties. We also provide our open-source code for the neural network many-body expansion, Tensormol.

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Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2017) · Communications of the ACM · doi:10.1145/3065386 · Cited by 112,155
Learning representations by back-propagating errors
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986) · Nature · doi:10.1038/323533a0 · Cited by 31,892
The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors
Boys, S. F., & Bernardi, F. (1970) · Molecular Physics · doi:10.1080/00268977000101561 · Cited by 22,304
Unsupervised representation learning with deep convolutional generative adversarial networks
Radford, A., Metz, L., & Chintala, S. (2015) · arXiv · doi:10.48550/arxiv.1511.06434 · Cited by 12,235
Improved Techniques for Training GANs
Salimans, T., Goodfellow, I., Zaremba, W., Cheung, V., Radford, A., & Chen, X. (2016) · arXiv · doi:10.48550/arxiv.1606.03498 · Cited by 6,965
Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces
Behler, J., & Parrinello, M. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.146401 · Cited by 5,010 · cited 1×
“Many diﬀerent chemical descriptors have been proposed, including the Coulomb matrix 70–72 , symmetry functions 13,14 , bispectrum 73,74 , permutation invariant polynomials 15,18 , metric ﬁngerprints 75–77 and the radial distribution Fourier series, 78 which is based on the electronic density and is…”
Background
Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons
Bartók, A. P., Payne, M. C., Kondor, R., & Csányi, G. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.136403 · Cited by 3,242
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package
Shao, Y., Gan, Z., Epifanovsky, E., Gilbert, A. T. B., Wormit, M., Kußmann, J., Lange, A. W., Behn, A., Deng, J., Feng, X., et al. (2014) · Molecular Physics · doi:10.1080/00268976.2014.952696 · Cited by 3,007
Self-citation
On representing chemical environments
Bartók, A. P., Kondor, R., & Csányi, G. (2013) · Physical Review B · doi:10.1103/physrevb.87.184115 · Cited by 2,572
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Rupp, M., Tkatchenko, A., Müller, K.-R., & von Lilienfeld, O. A. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.058301 · Cited by 2,312
ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost
Smith, J. S., Isayev, O., & Roitberg, A. E. (2017) · Chemical Science · doi:10.1039/c6sc05720a · Cited by 1,921
Atom-centered symmetry functions for constructing high-dimensional neural network potentials
Behler, J. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3553717 · Cited by 1,663
Quantum-chemical insights from deep tensor neural networks
Schütt, K. T., Arbabzadah, F., Chmiela, S., Müller, K. R., & Tkatchenko, A. (2017) · Nature Communications · doi:10.1038/ncomms13890 · Cited by 1,445
Current Status of the AMOEBA Polarizable Force Field
Ponder, J. W., Wu, C., Ren, P., Pande, V. S., Chodera, J. D., Schnieders, M. J., Haque, I., Mobley, D. L., Lambrecht, D. S., DiStasio, R. A., et al. (2010) · The Journal of Physical Chemistry B · doi:10.1021/jp910674d · Cited by 1,440
The elements of statistical learning: Data mining, inference, and prediction
Franklin, J. (2005) · The Mathematical Intelligencer · doi:10.1007/bf02985802 · Cited by 1,400
Improving deep neural networks for LVCSR using rectified linear units and dropout
Dahl, G. E., Sainath, T. N., & Hinton, G. E. (2013) · 2013 IEEE International Conference on Acoustics, Speech and Signal Processing · doi:10.1109/icassp.2013.6639346 · Cited by 1,310
Machine learning of accurate energy-conserving molecular force fields
Chmiela, S., Tkatchenko, A., Sauceda, H. E., Poltavsky, I., Schütt, K. T., & Müller, K. (2017) · Science Advances · doi:10.1126/sciadv.1603015 · Cited by 1,237
Fragmentation Methods: A Route to Accurate Calculations on Large Systems
Gordon, M. S., Fedorov, D. G., Pruitt, S. R., & Slipchenko, L. V. (2011) · Chemical Reviews · doi:10.1021/cr200093j · Cited by 1,110
Accelerating materials property predictions using machine learning
Pilania, G., Wang, C., Jiang, X., Rajasekaran, S., & Ramprasad, R. (2013) · Scientific Reports · doi:10.1038/srep02810 · Cited by 871
Machine learning predictions of molecular properties: Accurate many-body potentials and nonlocality in chemical space
Hansen, K., Biegler, F., Ramakrishnan, R., Pronobis, W., von Lilienfeld, O. A., Müller, K.-R., & Tkatchenko, A. (2015) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.5b00831 · Cited by 815
Neural network potential-energy surfaces in chemistry: a tool for large-scale simulations
Behler, J. (2011) · Physical Chemistry Chemical Physics · doi:10.1039/c1cp21668f · Cited by 781 · cited 1×
“Many diﬀerent chemical descriptors have been proposed, including the Coulomb matrix 70–72 , symmetry functions 13,14 , bispectrum 73,74 , permutation invariant polynomials 15,18 , metric ﬁngerprints 75–77 and the radial distribution Fourier series, 78 which is based on the electronic density and is…”
Background
Polarizable Atomic Multipole-Based AMOEBA Force Field for Proteins
Shi, Y., Xia, Z., Zhang, J., Best, R. B., Wu, C., Ponder, J. W., & Ren, P. Y. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct4003702 · Cited by 718
Ab initio studies of cyclic water clusters (H2O)n, n=1–6. II. Analysis of many-body interactions
Xantheas, S. S. (1994) · The Journal of Chemical Physics · doi:10.1063/1.466846 · Cited by 717 · cited 1×
“High order terms are more costly calculations and the error of the MBE is often balanced with the error of the underlying model chemistry at third order 22–24 so long as care is taken to correct for basis set superposition error (BSSE).”
Background
Machine learning of molecular electronic properties in chemical compound space
Montavon, G., Rupp, M., Gobre, V., Vázquez‐Mayagoitia, Á., Hansen, K., Tkatchenko, A., Müller, K.-R., & von Lilienfeld, O. A. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/9/095003 · Cited by 683
Is the Ewald summation still necessary? Pairwise alternatives to the accepted standard for long-range electrostatics
Fennell, C. J., & Gezelter, J. D. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2206581 · Cited by 676
The Harvard Clean Energy Project: Large-Scale Computational Screening and Design of Organic Photovoltaics on the World Community Grid
Hachmann, J., Olivares‐Amaya, R., Atahan-Evrenk, Ş., Amador‐Bedolla, C., Sánchez‐Carrera, R. S., Gold‐Parker, A., Vogt-Maranto, L., Brockway, A. M., & Aspuru‐Guzik, A. (2011) · The Journal of Physical Chemistry Letters · doi:10.1021/jz200866s · Cited by 668 · cited 1×
“It has also been used to construct kinetic energy functionals 48–50 and to design new materials 44,51–54 .”
Method
Finding Density Functionals with Machine Learning
Snyder, J. C., Rupp, M., Hansen, K., Müller, K., & Burke, K. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.253002 · Cited by 649
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Finding Nature’s Missing Ternary Oxide Compounds Using Machine Learning and Density Functional Theory
Hautier, G., Fischer, C. C., Jain, A., Mueller, T., & Ceder, G. (2010) · Chemistry of Materials · doi:10.1021/cm100795d · Cited by 580
Permutation invariant polynomial neural network approach to fitting potential energy surfaces
Jiang, B., & Guo, H. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4817187 · Cited by 542
Cooperativity and hydrogen bonding network in water clusters
Xantheas, S. S. (2000) · Chemical Physics · doi:10.1016/s0301-0104(00)00189-0 · Cited by 482
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Ren, P. Y., Wu, C., & Ponder, J. W. (2011) · Journal of Chemical Theory and Computation · doi:10.1021/ct200304d · Cited by 474
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Schütt, K. T., Glawe, H., Brockherde, F., Sanna, A., Müller, K. R., & Gross, E. K. U. (2014) · Physical Review B · doi:10.1103/physrevb.89.205118 · Cited by 467
Crystal structure representations for machine learning models of formation energies
Faber, F. A., Lindmaa, A., von Lilienfeld, O. A., & Armiento, R. (2015) · International Journal of Quantum Chemistry · doi:10.1002/qua.24917 · Cited by 466
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Ma, X., Li, Z., Achenie, L. E. K., & Xin, H. (2015) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.5b01660 · Cited by 430
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Khaliullin, R. Z., Eshet, H., Kühne, T. D., Behler, J., & Parrinello, M. (2011) · Nature Materials · doi:10.1038/nmat3078 · Cited by 370
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Rupp, M. (2015) · International Journal of Quantum Chemistry · doi:10.1002/qua.24954 · Cited by 366
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Song, S., & Xiao, J. (2014) · Lecture notes in computer science · doi:10.1007/978-3-319-10599-4_41 · Cited by 361
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Handley, C. M., & Popelier, P. L. A. (2010) · The Journal of Physical Chemistry A · doi:10.1021/jp9105585 · Cited by 324
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Yoo, D., Kim, N. I., Park, S., Paek, A. S., & Kweon, I. S. (2016) · Lecture notes in computer science · doi:10.1007/978-3-319-46484-8_31 · Cited by 313
Evolutionary approach for determining first-principles hamiltonians
Hart, G. L. W., Blüm, V., Walorski, M. J., & Zunger, A. (2005) · Nature Materials · doi:10.1038/nmat1374 · Cited by 308
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Ghasemi, S. A., Hofstetter, A., Saha, S., & Goedecker, S. (2015) · Physical Review B · doi:10.1103/physrevb.92.045131 · Cited by 293
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Raghavachari, K., & Saha, A. (2015) · Chemical Reviews · doi:10.1021/cr500606e · Cited by 290 · cited 1×
“In insulators the high-order terms of the MBE decay rapidly with distance, which makes this type of approximation useful for low-scaling, high-accuracy models of liquids, solids and biological molecules 1–11 .”
Background
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Hachmann, J., Olivares‐Amaya, R., Jinich, A., Appleton, A. L., Blood-Forsythe, M. A., Seress, L. R., Román-Salgado, C., Trepte, K., Atahan-Evrenk, Ş., Er, S., et al. (2013) · Energy & Environmental Science · doi:10.1039/c3ee42756k · Cited by 246
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von Lilienfeld, O. A., & Tkatchenko, A. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3432765 · Cited by 239
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Im, D. J., Kim, C. D., Jiang, H., & Memisevic, R. (2016) · arXiv.org · doi:10.48550/arxiv.1602.05110 · Cited by 232
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Richard, R. M., & Herbert, J. M. (2012) · The Journal of Chemical Physics · doi:10.1063/1.4742816 · Cited by 226 · cited 3×
“3,6,9,21 .”
Background
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von Lilienfeld, O. A., Ramakrishnan, R., Rupp, M., & Knoll, A. M. (2015) · International Journal of Quantum Chemistry · doi:10.1002/qua.24912 · Cited by 225 · cited 1×
“…functions 13,14 , bispectrum 73,74 , permutation invariant polynomials 15,18 , metric ﬁngerprints 75–77 and the radial distribution Fourier series, 78 which is based on the electronic density and is similar to a descriptor our group has used in the past for learning kinetic functionals 50 .”
Method
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Manzhos, S., Dawes, R., & Carrington, T. (2014) · International Journal of Quantum Chemistry · doi:10.1002/qua.24795 · Cited by 205
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Bartók, A. P., Gillan, M. J., Manby, F. R., & Cśanyi, G. (2013) · Physical Review B · doi:10.1103/physrevb.88.054104 · Cited by 202
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Manzhos, S., & Carrington, T. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2387950 · Cited by 184
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Kiwiel, K. C. (2001) · Mathematical Programming · doi:10.1007/pl00011414 · Cited by 184
Interaction energies of large clusters from many-body expansion
Góra, U., Podeszwa, R., Cencek, W., & Szalewicz, K. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3664730 · Cited by 167
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Blüm, V., Hart, G. L. W., Walorski, M. J., & Zunger, A. (2005) · Physical Review B · doi:10.1103/physrevb.72.165113 · Cited by 153
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Dahlke, E. E., & Truhlar, D. G. (2007) · Journal of Chemical Theory and Computation · doi:10.1021/ct700057x · Cited by 147 · cited 2×
“27,57 .”
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Medders, G. R., Babin, V., & Paesani, F. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct300913g · Cited by 145
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Sadeghi, A., Ghasemi, S. A., Schaefer, B., Mohr, S., Lill, M. A., & Goedecker, S. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4828704 · Cited by 141
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Snyder, J. C., Rupp, M., Hansen, K., Blooston, L., Müller, K., & Burke, K. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4834075 · Cited by 138
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Richard, R. M., Lao, K. U., & Herbert, J. M. (2014) · Accounts of Chemical Research · doi:10.1021/ar500119q · Cited by 134 · cited 1×
“The integral precision and SCF convergence criteria were as tight as possible 62,63 and BSSE using the K-mer centered basis set approach ( k − CBS ) 58 was applied. are Training and test geometries drawn from an AMBER molecular dynamics trajectory 64–67 of 108 methanol molecules at 330 K and…”
Method
Practical quantum mechanics-based fragment methods for predicting molecular crystal properties
Wen, S., Nanda, K. D., Huang, Y., & Beran, G. J. O. (2012) · Physical Chemistry Chemical Physics · doi:10.1039/c2cp23949c · Cited by 133
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Yao, K., & Parkhill, J. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b01011 · Cited by 130
Self-citation
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Zhu, L., Amsler, M., Fuhrer, T., Schaefer, B., Faraji, S., Rostami, S., Ghasemi, S. A., Sadeghi, A., Grauzinyte, M., Wolverton, C., et al. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4940026 · Cited by 128
Understanding the many-body expansion for large systems. I. Precision considerations
Richard, R. M., Lao, K. U., & Herbert, J. M. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4885846 · Cited by 125
Many-Overlapping-Body (MOB) Expansion: A Generalized Many Body Expansion for Nondisjoint Monomers in Molecular Fragmentation Calculations of Covalent Molecules
Mayhall, N. J., & Raghavachari, K. (2012) · Journal of Chemical Theory and Computation · doi:10.1021/ct300366e · Cited by 125 · cited 2×
“The closest work predicted the many-body energy of Si n ( n = 1 , 2 , ... 7) 55 clusters.”
Background
Communication: An accurate global potential energy surface for the OH + CO → H + CO2 reaction using neural networks
Chen, J., Xu, X., Xu, X., & Zhang, D. H. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4811109 · Cited by 114
Approximating quantum many-body intermolecular interactions in molecular clusters using classical polarizable force fields
Beran, G. J. O. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3121323 · Cited by 112 · cited 1×
“3,6,9,21 .”
Using neural networks, optimized coordinates, and high-dimensional model representations to obtain a vinyl bromide potential surface
Manzhos, S., & Carrington, T. (2008) · The Journal of Chemical Physics · doi:10.1063/1.3021471 · Cited by 111
On the representation of many-body interactions in water
Medders, G. R., Götz, A. W., Morales, M. A., Bajaj, P., & Paesani, F. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4930194 · Cited by 106
Theoretical Characterization of the (H2O)21 Cluster: Application of an n-body Decomposition Procedure
Cui, J. X., Liu, H., & Jordan, K. D. (2006) · The Journal of Physical Chemistry B · doi:10.1021/jp056416m · Cited by 102
Understanding the many-body expansion for large systems. II. Accuracy considerations
Lao, K. U., Liu, K., Richard, R. M., & Herbert, J. M. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4947087 · Cited by 99 · cited 1×
“3,28,29 Statistical models from machine learning are becoming popular chemical models.”
Learning Invariant Representations of Molecules for Atomization Energy Prediction
Montavon, G., Hansen, K., Fazli, S., Biegler, F., Ziehe, A., Tkatchenko, A., von Lilienfeld, O. A., & Müller, K.-R. (2014) · Cited by 97
Convergence of the many-body expansion of interaction potentials: From van der Waals to covalent and metallic systems
Hermann, A., Krawczyk, R. P., Lein, M., Schwerdtfeger, P., Hamilton, I. P., & Stewart, J. J. P. (2007) · Physical Review A · doi:10.1103/physreva.76.013202 · Cited by 83
Convergence of theab initiomany-body expansion for the cohesive energy of solid mercury
Paulus, B., Rościszewski, K., Gaston, N., Schwerdtfeger, P., & Stoll, H. (2004) · Physical Review B · doi:10.1103/physrevb.70.165106 · Cited by 82
A permutationally invariant full-dimensional ab initio potential energy surface for the abstraction and exchange channels of the H + CH4 system
Li, J., Chen, J., Zhao, Z., Xie, D., Zhang, D. H., & Guo, H. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4921412 · Cited by 77
Modeling electronic quantum transport with machine learning
López‐Bezanilla, A., & von Lilienfeld, O. A. (2014) · Physical Review B · doi:10.1103/physrevb.89.235411 · Cited by 72
Permutationally Invariant Fitting of Many-Body, Non-covalent Interactions with Application to Three-Body Methane–Water–Water
Conte, R., Qu, C., & Bowman, J. M. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b00091 · Cited by 71 · cited 1×
“36 Permutationally invariant polynomials have been used to express the many-body energies of water clusters 10,36 and water-methane clusters 37 with great success.”
Method
Pair–Pair Approximation to the Generalized Many-Body Expansion: An Alternative to the Four-Body Expansion for ab Initio Prediction of Protein Energetics via Molecular Fragmentation
Liu, J., & Herbert, J. M. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b00955 · Cited by 68
Development of generalized potential-energy surfaces using many-body expansions, neural networks, and moiety energy approximations
Malshe, M., Narulkar, R., Raff, L. M., Hagan, M., Bukkapatnam, S., Agrawal, P. M., & Komanduri, R. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3124802 · Cited by 66
Many-Body Expansion with Overlapping Fragments: Analysis of Two Approaches
Richard, R. M., & Herbert, J. M. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct300985h · Cited by 66 · cited 1×
“3,28,29 Statistical models from machine learning are becoming popular chemical models.”
Background
Many-body interaction analysis: Algorithm development and application to large molecular clusters
Kulkarni, A. D., Ganesh, V., & Gadre, S. R. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1780156 · Cited by 65
Ab InitioQuality NMR Parameters in Solid-State Materials Using a High-Dimensional Neural-Network Representation
Cuny, J., Xie, Y., Pickard, C. J., & Hassanali, A. A. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b01006 · Cited by 65
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Trouble with the Many-Body Expansion
Ouyang, J. F., Cvitkovic, M. W., & Bettens, R. P. A. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct500396b · Cited by 61 · cited 1×
“25,26 An electrostatically embedded MBE (EE-MBE) has also been proposed as a means to improve the accuracy.”
Accurate Localization of 3D Objects from RGB-D Data Using Segmentation Hypotheses
Kim, B.-S., Xu, S., & Savarese, S. (2013) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2013.409 · Cited by 60 · cited 1×
“82 An example D-map can be seen in Figure 1.”
Background
Fitting sparse multidimensional data with low-dimensional terms
Manzhos, S., Yamashita, K., & Carrington, T. (2009) · Computer Physics Communications · doi:10.1016/j.cpc.2009.05.022 · Cited by 58
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“3,6,9,21 .”
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Authors: Yao, K., Herr, J. E., & Parkhill, J.
Affiliations: University of Notre Dame (US)
ORCID: Yao, Kun
Herr, John E.
Parkhill, John
Venue: The Journal of Chemical Physics
Publisher: AIP Publishing
Published: 2017-01-04
Volume: 146
Issue: 1
Pages: 014106-014106
ISSN: 0021-9606 (ISSN-L)
1089-7690
DOI: 10.1063/1.4973380
OpenAlex: W2526734845
Cited by: 120
References: 106
Citations by year: 2026: 4 · 2025: 10 · 2024: 4 · 2023: 11 · 2022: 10 · 2021: 6 · 2020: 18 · 2019: 16 · 2018: 25 · 2017: 16
FWCI: 10.06
Type: journal article
Language: en
Open access: green
arxiv.org
Locations: The Journal of Chemical Physics (publishedVersion)
PubMed (publishedVersion)
arXiv (Cornell University) (submittedVersion)
arXiv (Cornell University)
Funders: UND chemistry dept startup funds
Topics: Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
Life Sciences › Pharmacology, Toxicology and Pharmaceutics › Drug Discovery › Computational Drug Discovery Methods
Keywords: many-body expansion, artificial neural networks, ab initio potential energy surface, fragmentation methods, large-scale quantum chemistry, computational scaling, methanol, molecular property prediction

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The many-body expansion combined with neural networks

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