Ab initio quantum chemistry with neural-network wavefunctions.
Journal
Nature reviews. Chemistry
ISSN: 2397-3358
Titre abrégé: Nat Rev Chem
Pays: England
ID NLM: 101703631
Informations de publication
Date de publication:
Oct 2023
Oct 2023
Historique:
accepted:
16
06
2023
pubmed:
10
8
2023
medline:
10
8
2023
entrez:
9
8
2023
Statut:
ppublish
Résumé
Deep learning methods outperform human capabilities in pattern recognition and data processing problems and now have an increasingly important role in scientific discovery. A key application of machine learning in molecular science is to learn potential energy surfaces or force fields from ab initio solutions of the electronic Schrödinger equation using data sets obtained with density functional theory, coupled cluster or other quantum chemistry (QC) methods. In this Review, we discuss a complementary approach using machine learning to aid the direct solution of QC problems from first principles. Specifically, we focus on quantum Monte Carlo methods that use neural-network ansatzes to solve the electronic Schrödinger equation, in first and second quantization, computing ground and excited states and generalizing over multiple nuclear configurations. Although still at their infancy, these methods can already generate virtually exact solutions of the electronic Schrödinger equation for small systems and rival advanced conventional QC methods for systems with up to a few dozen electrons.
Identifiants
pubmed: 37558761
doi: 10.1038/s41570-023-00516-8
pii: 10.1038/s41570-023-00516-8
doi:
Types de publication
Journal Article
Review
Langues
eng
Sous-ensembles de citation
IM
Pagination
692-709Informations de copyright
© 2023. Springer Nature Limited.
Références
Carleo, G. et al. Machine learning and the physical sciences. Rev. Mod. Phys. 91, 045002 (2019).
doi: 10.1103/RevModPhys.91.045002
Jumper, J. et al. Highly accurate protein structure prediction with AlphaFold. Nature 596, 583–589 (2021).
pubmed: 34265844
pmcid: 8371605
doi: 10.1038/s41586-021-03819-2
Deringer, V. L. et al. Origins of structural and electronic transitions in disordered silicon. Nature 589, 59–64 (2021).
pubmed: 33408379
doi: 10.1038/s41586-020-03072-z
Noé, F., Olsson, S., Köhler, J. & Wu, H. Boltzmann generators: sampling equilibrium states of many-body systems with deep learning. Science 365, eaaw1147 (2019).
pubmed: 31488660
doi: 10.1126/science.aaw1147
Huang, B. & von Lilienfeld, O. A. Quantum machine learning using atom-in-molecule-based fragments selected on the fly. Nat. Chem. 12, 945–951 (2020).
pubmed: 32929248
doi: 10.1038/s41557-020-0527-z
Tkatchenko, A. Machine learning for chemical discovery. Nat. Commun. 11, 4125 (2020).
pubmed: 32807794
pmcid: 7431574
doi: 10.1038/s41467-020-17844-8
von Lilienfeld, O. A. & Burke, K. Retrospective on a decade of machine learning for chemical discovery. Nat. Commun. 11, 4895 (2020).
doi: 10.1038/s41467-020-18556-9
Noé, F., Tkatchenko, A., Müller, K.-R. & Clementi, C. Machine learning for molecular simulation. Annu. Rev. Phys. Chem. 71, 361–390 (2020).
pubmed: 32092281
doi: 10.1146/annurev-physchem-042018-052331
Dral, P. O. Quantum chemistry in the age of machine learning. J. Phys. Chem. Lett. 11, 2336–2347 (2020).
pubmed: 32125858
doi: 10.1021/acs.jpclett.9b03664
Unke, O. T. et al. Machine learning force fields. Chem. Rev. 121, 10142–10186 (2021).
pubmed: 33705118
pmcid: 8391964
doi: 10.1021/acs.chemrev.0c01111
von Lilienfeld, O. A., Müller, K.-R. & Tkatchenko, A. Exploring chemical compound space with quantum-based machine learning. Nat. Rev. Chem. 4, 347–358 (2020).
doi: 10.1038/s41570-020-0189-9
Bian, Y. & Xie, X.-Q. Generative chemistry: drug discovery with deep learning generative models. J. Mol. Model. 27, 71 (2021).
pubmed: 33543405
doi: 10.1007/s00894-021-04674-8
Jones, R. O. Density functional theory: its origins, rise to prominence, and future. Rev. Mod. Phys. 87, 897–923 (2015).
doi: 10.1103/RevModPhys.87.897
Bartlett, R. J. & Musiał, M. Coupled-cluster theory in quantum chemistry. Rev. Mod. Phys. 79, 291–352 (2007).
doi: 10.1103/RevModPhys.79.291
Deringer, V. L. et al. Gaussian process regression for materials and molecules. Chem. Rev. 121, 10073–10141 (2021).
pubmed: 34398616
pmcid: 8391963
doi: 10.1021/acs.chemrev.1c00022
Behler, J. Four generations of high-dimensional neural network potentials. Chem. Rev. 121, 10037–10072 (2021).
pubmed: 33779150
doi: 10.1021/acs.chemrev.0c00868
Musil, F. et al. Physics-inspired structural representations for molecules and materials. Chem. Rev. 121, 9759–9815 (2021).
pubmed: 34310133
doi: 10.1021/acs.chemrev.1c00021
Li, H., Collins, C., Tanha, M., Gordon, G. J. & Yaron, D. J. A density functional tight binding layer for deep learning of chemical Hamiltonians. J. Chem. Theory Comput. 14, 5764–5776 (2018).
pubmed: 30351008
doi: 10.1021/acs.jctc.8b00873
Schütt, K. T., Gastegger, M., Tkatchenko, A., Müller, K.-R. & Maurer, R. J. Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions. Nat. Commun. 10, 5024 (2019).
pubmed: 31729373
pmcid: 6858523
doi: 10.1038/s41467-019-12875-2
Kirkpatrick, J. et al. Pushing the frontiers of density functionals by solving the fractional electron problem. Science 374, 1385–1389 (2021).
pubmed: 34882476
doi: 10.1126/science.abj6511
Chandrasekaran, A. et al. Solving the electronic structure problem with machine learning. Comput. Mater. 5, 1–7 (2019).
Welborn, M., Cheng, L. & Miller III, T. F. Transferability in machine learning for electronic structure via the molecular orbital basis. J. Chem. Theory Comput. 14, 4772–4779 (2018).
pubmed: 30040892
doi: 10.1021/acs.jctc.8b00636
Nagai, R., Akashi, R. & Sugino, O. Completing density functional theory by machine learning hidden messages from molecules. Comput. Mater. 6, 1–8 (2020).
Gómez-Bombarelli, R. et al. Automatic chemical design using a data-driven continuous representation of molecules. ACS Cent. Sci. 4, 268–276 (2018).
pubmed: 29532027
pmcid: 5833007
doi: 10.1021/acscentsci.7b00572
Hoogeboom, E., Satorras, V. G., Vignac, C. & Welling, M. Equivariant diffusion for molecule generation in 3D. Preprint at http://arxiv.org/abs/2203.17003 (2022).
Torlai, G. et al. Neural-network quantum state tomography. Nat. Phys. 14, 447–450 (2018).
doi: 10.1038/s41567-018-0048-5
Sutton, R. S. & Barto, A. G. Reinforcement Learning: An Introduction (MIT Press, 2018).
Tesauro, G. TD-Gammon, a self-teaching backgammon program, achieves master-level play. Neural Comput. 6, 215–219 (1994).
doi: 10.1162/neco.1994.6.2.215
Mnih, V. et al. Human-level control through deep reinforcement learning. Nature 518, 529–533 (2015).
pubmed: 25719670
doi: 10.1038/nature14236
Silver, D. et al. Mastering the game of Go with deep neural networks and tree search. Nature 529, 484–489 (2016).
pubmed: 26819042
doi: 10.1038/nature16961
Degrave, J. et al. Magnetic control of tokamak plasmas through deep reinforcement learning. Nature 602, 414–419 (2022).
pubmed: 35173339
pmcid: 8850200
doi: 10.1038/s41586-021-04301-9
Heinrich, J., Lanctot, M. & Silver, D. Fictitious self-play in extensive-form games. In Proceedings of the 32nd International Conference on Machine Learning 805–813 (PMLR, 2015).
Silver, D. et al. A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play. Science 362, 1140–1144 (2018).
pubmed: 30523106
doi: 10.1126/science.aar6404
Battaglia, S. Machine learning wavefunction. In Quantum Chemistry in the Age of Machine Learning 577–616 (Elsevier, 2023).
Manzhos, S. Machine learning for the solution of the Schrödinger equation. Mach. Learn. Sci. Techn. 1, 013002 (2020).
doi: 10.1088/2632-2153/ab7d30
Piela, L. Ideas of Quantum Chemistry 2nd edn (Elsevier, 2014).
Foulkes, W. M. C., Mitas, L., Needs, R. J. & Rajagopal, G. Quantum Monte Carlo simulations of solids. Rev. Mod. Phys. 73, 33–83 (2001).
doi: 10.1103/RevModPhys.73.33
Bajdich, M., Mitas, L., Drobný, G., Wagner, L. K. & Schmidt, K. E. Pfaffian pairing wave functions in electronic-structure quantum Monte Carlo Simulations. Phys. Rev. Lett. 96, 130201 (2006).
pubmed: 16711968
doi: 10.1103/PhysRevLett.96.130201
Han, J., Zhang, L. & Weinan, E. Solving many-electron Schrödinger equation using deep neural networks. J. Comput. Phys. 399, 108929 (2019).
doi: 10.1016/j.jcp.2019.108929
Acevedo, A., Curry, M., Joshi, S. H., Leroux, B. & Malaya, N. Vandermonde wave function ansatz for improved variational Monte Carlo. In 2020 IEEE/ACM Fourth Workshop on Deep Learning on Supercomputers (DLS) 40–47 (IEEE, 2020).
Szabo, A. & Ostlund, N. S. Modern Quantum Chemistry (Dover Publications, 1996).
Becca, F. & Sorella, S. Quantum Monte Carlo Approaches for Correlated Systems 1st edn (Cambridge Univ. Press, 2017).
Teale, A. M. et al. DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science. Phys. Chem. Chem. Phys. 24, 28700–28781 (2022).
pubmed: 36269074
pmcid: 9728646
doi: 10.1039/D2CP02827A
Chan, G. K.-L. & Sharma, S. The density matrix renormalization group in quantum chemistry. Annu. Rev. Phys. Chem. 62, 465 (2011).
pubmed: 21219144
doi: 10.1146/annurev-physchem-032210-103338
Huron, B., Malrieu, J. P. & Rancurel, P. Iterative perturbation calculations of ground and excited state energies from multiconfigurational zeroth-order wavefunctions. J. Chem. Phys. 58, 5745–5759 (1973).
doi: 10.1063/1.1679199
Booth, G. H., Thom, A. J. W. & Alavi, A. Fermion Monte Carlo without fixed nodes: a game of life, death, and annihilation in Slater determinant space. J. Chem. Phys. 131, 054106 (2009).
pubmed: 19673550
doi: 10.1063/1.3193710
Olsen, J. The CASSCF method: a perspective and commentary: CASSCF Method. Int. J. Quantum Chem. 111, 3267–3272 (2011).
doi: 10.1002/qua.23107
Carleo, G. & Troyer, M. Solving the quantum many-body problem with artificial neural networks. Science 355, 602–606 (2017).
pubmed: 28183973
doi: 10.1126/science.aag2302
Saito, H. Solving the Bose–Hubbard model with machine learning. J. Phys. Soc. Jpn. 86, 093001 (2017).
doi: 10.7566/JPSJ.86.093001
Nomura, Y., Darmawan, A. S., Yamaji, Y. & Imada, M. Restricted Boltzmann machine learning for solving strongly correlated quantum systems. Phys. Rev. B 96, 205152 (2017).
doi: 10.1103/PhysRevB.96.205152
Adams, C., Carleo, G., Lovato, A. & Rocco, N. Variational Monte Carlo calculations of A≤4 nuclei with an artificial neural-network correlator ansatz. Phys. Rev. Lett. 127, 022502 (2021).
pubmed: 34296893
doi: 10.1103/PhysRevLett.127.022502
Astrakhantsev, N. et al. Broken-symmetry ground states of the Heisenberg model on the pyrochlore lattice. Phys. Rev. X 11, 041021 (2021).
Perronnin, F., Liu, Y., Sánchez, J. & Poirier, H. Large-scale image retrieval with compressed fisher vectors. In 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition 3384–3391 (IEEE, 2010).
Krizhevsky, A., Sutskever, I. & Hinton, G. E. Imagenet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems Vol. 25, 1097–1105 (Curran Associates, 2012).
Schmidhuber, J. Deep learning in neural networks: an overview. Neural Netw. 61, 85–117 (2015).
pubmed: 25462637
doi: 10.1016/j.neunet.2014.09.003
LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015).
pubmed: 26017442
doi: 10.1038/nature14539
McCulloch, W. S. & Pitts, W. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5, 115–133 (1943).
doi: 10.1007/BF02478259
Rosenblatt, F. The perceptron: a probabilistic model for information storage and organization in the brain. Psychol. Rev. 65, 386 (1958).
pubmed: 13602029
doi: 10.1037/h0042519
Hornik, K., Stinchcombe, M. & White, H. Multilayer feedforward networks are universal approximators. Neural Netw. 2, 359–366 (1989).
doi: 10.1016/0893-6080(89)90020-8
Werbos, P. Beyond regression: new tools for prediction and analysis in the behavioral sciences. PhD thesis. Harvard Univ. (1974).
Linnainmaa, S. The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors. Master’s thesis (in Finnish), Univ. Helsinki (1970).
Linnainmaa, S. Taylor expansion of the accumulated rounding error. BIT Numer. Math. 16, 146–160 (1976).
doi: 10.1007/BF01931367
Rumelhart, D. E., Hinton, G. E. & Williams, R. J. Learning representations by back-propagating errors. Nature 323, 533–536 (1986).
doi: 10.1038/323533a0
Glorot, X. & Bengio, Y. Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the 13th International Conference on Artificial Intelligence and Statistics 249–256 (PMLR, 2010).
Hooker, S. The hardware lottery. Commun. ACM 64, 58–65 (2021).
doi: 10.1145/3467017
Dauphin, Y. et al. Identifying and attacking the saddle point problem in high-dimensional non-convex optimization. In Advances in Neural Information Processing Systems Vol. 27, 2933–2941 (Curran Associates, 2014).
Choromanska, A., Henaff, M., Mathieu, M., Arous, G. B. & LeCun, Y. The loss surfaces of multilayer networks. In Proceedings of the 18th International Conference on Artificial Intelligence and Statistics 192–204 (PMLR, 2015).
Bottou, L. & Bousquet, O. Learning using large datasets. In Mining Massive Data Sets for Security 15–26 (IOS Press, 2008).
Bottou, L. & Bousquet, O. The tradeoffs of large-scale learning. In Optimization for Machine Learning, 351–368 (MIT Press, 2011).
Russakovsky, O. et al. ImageNet large scale visual recognition challenge. Int. J. Comput. Vis. 115, 211–252 (2015).
doi: 10.1007/s11263-015-0816-y
Abadi, M. et al. TensorFlow: a system for large-scale machine learning. In Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation 265–283 (USENIX Association, 2016).
Paszke, A. et al. Automatic differentiation in PyTorch. In NIPS Workshop on Automatic Differentiation (2017).
Bradbury, J. et al. JAX: Composable Transformations of Python+ NumPy Programs (GitHub, 2018); https://github.com/google/jax .
Goodfellow, I. J., Shlens, J. & Szegedy, C. Explaining and harnessing adversarial examples. Third International Conference on Learning Representations (ICLR) (ICLR, 2015).
LeCun, Y., Bottou, L., Bengio, Y. & Haffner, P. Gradient-based learning applied to document recognition. Proc. IEEE 86, 2278–2324 (1998).
doi: 10.1109/5.726791
Shawe-Taylor, J. Building symmetries into feedforward networks. In 1989 First IEE International Conference on Artificial Neural Networks 158–162 (IET, 1989).
Vaswani, A. et al. Attention is all you need. In Advances in Neural Information Processing Systems Vol. 30, 5998–6008 (Curran Associates, 2017).
Schütt, K. T., Sauceda, H. E., Kindermans, P.-J., Tkatchenko, A. & Müller, K.-R. SchNet — a deep learning architecture for molecules and materials. J. Chem. Phys. 148, 241722 (2018).
pubmed: 29960322
doi: 10.1063/1.5019779
Bronstein, M. M., Bruna, J., Cohen, T. & Veličković, P. Geometric deep learning: grids, groups, graphs, geodesics, and gauges. Preprint at http://arxiv.org/abs/2104.13478 (2021).
Hinton, G. E. & Salakhutdinov, R. R. Reducing the dimensionality of data with neural networks. Science 313, 504–507 (2006).
pubmed: 16873662
doi: 10.1126/science.1127647
Kingma, D. P. & Welling, M. Auto-encoding variational Bayes. Preprint at http://arxiv.org/abs/1312.6114 (2013).
Goodfellow, I. et al. Generative adversarial nets. In Advances in Neural Information Processing Systems Vol. 27, 2672–2680 (Curran Associates, 2014).
Rezende, D. & Mohamed, S. Variational inference with normalizing flows. In Proceedings of the 32nd International Conference on Machine Learning 1530–1538 (PMLR, 2015).
van den Oord, A. et al. WaveNet: a generative model for raw audio. Preprint at http://arxiv.org/abs/1609.3499 (2016).
van den Oord, A. et al. Conditional image generation with PixelCNN decoders. In Advances in Neural Information Processing Systems Vol. 29, 4797–4805 (Curran Associates, 2016).
Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N. & Ganguli, S. Deep unsupervised learning using nonequilibrium thermodynamics. In Proceedings of the 32nd International Conference on Machine Learning 2256–2265 (PMLR, 2015).
Sharir, O., Levine, Y., Wies, N., Carleo, G. & Shashua, A. Deep autoregressive models for the efficient variational simulation of many-body quantum systems. Phys. Rev. Lett. 124, 020503 (2020).
pubmed: 32004039
doi: 10.1103/PhysRevLett.124.020503
Choo, K., Neupert, T. & Carleo, G. Two-dimensional frustrated J
doi: 10.1103/PhysRevB.100.125124
Hibat-Allah, M., Ganahl, M., Hayward, L. E., Melko, R. G. & Carrasquilla, J. Recurrent neural network wave functions. Phys. Rev. Res. 2, 023358 (2020).
Xie, H., null, L. Z. & Wang, L. Ab-initio study of interacting fermions at finite temperature with neural canonical transformation. J. Mach. Learn. 1, 38 (2022).
doi: 10.4208/jml.220113
Behler, J. & Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007).
pubmed: 17501293
doi: 10.1103/PhysRevLett.98.146401
Rupp, M., Tkatchenko, A., Müller, K.-R. & von Lilienfeld, O. A. Fast and accurate modeling of molecular atomization energies with machine learning. Phys. Rev. Lett. 108, 058301 (2012).
pubmed: 22400967
doi: 10.1103/PhysRevLett.108.058301
Bartók, A. P., Kondor, R. & Csányi, G. On representing chemical environments. Phys. Rev. B 87, 184115 (2013).
doi: 10.1103/PhysRevB.87.184115
Schütt, K. T., Arbabzadah, F., Chmiela, S., Müller, K. R. & Tkatchenko, A. Quantum-chemical insights from deep tensor neural networks. Nat. Commun. 8, 13890 (2017).
pubmed: 28067221
pmcid: 5228054
doi: 10.1038/ncomms13890
Thomas, N. et al. Tensor field networks: rotation- and translation-equivariant neural networks for 3D point clouds. Preprint at https://arxiv.org/abs/1802.08219 (2018).
Schütt, K. T., Unke, O. T. & Gastegger, M. Equivariant message passing for the prediction of tensorial properties and molecular spectra. In Proceedings of the 38th International Conference on Machine Learning 9377–9388 (PMLR, 2021).
Miller, B. K., Geiger, M., Smidt, T. E. & Noé, F. Relevance of rotationally equivariant convolutions for predicting molecular properties. Preprint at https://arxiv.org/abs/2008.08461 (2020).
Geiger, M. & Smidt, T. e3nn: Euclidean neural networks. Preprint at http://arxiv.org/abs/2207.09453 (2022).
Batzner, S. E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nat. Commun. 13, 2453 (2022).
Batatia, I., Kovács, D. P., Simm, G. N., Ortner, C. & Csányi, G. MACE: higher order equivariant message passing neural networks for fast and accurate force fields. In Advances in Neural Information Processing Systems Vol. 35, 11423–11436 (Curran Associates, 2022).
Huang, X., Braams, B. J. & Bowman, J. M. Ab initio potential energy and dipole moment surfaces for H5O2+. J. Chem. Phys. 122, 44308 (2005).
pubmed: 15740249
doi: 10.1063/1.1834500
Drautz, R. Atomic cluster expansion for accurate and transferable interatomic potentials. Phys. Rev. B 99, 014104 (2019).
doi: 10.1103/PhysRevB.99.014104
Allen, A. E. A., Dusson, G., Ortner, C. & Csányi, G. Atomic permutationally invariant polynomials for fitting molecular force fields. Mach. Learn.: Sci. Tech. 2, 025017 (2021).
Benali, A. et al. Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids — A case study in diamond. J. Chem. Phys. 153, 184111 (2020).
pubmed: 33187421
doi: 10.1063/5.0021036
Stokes, J., Izaac, J., Killoran, N. & Carleo, G. Quantum natural gradient. Quantum 4, 269 (2020).
doi: 10.22331/q-2020-05-25-269
Feynman, R. P. & Cohen, M. Energy spectrum of the excitations in liquid helium. Phys. Rev. 102, 1189–1204 (1956).
doi: 10.1103/PhysRev.102.1189
Kwon, Y., Ceperley, D. M. & Martin, R. M. Effects of three-body and backflow correlations in the two-dimensional electron gas. Phys. Rev. B 48, 12037–12046 (1993).
doi: 10.1103/PhysRevB.48.12037
Tocchio, L. F., Becca, F., Parola, A. & Sorella, S. Role of backflow correlations for the nonmagnetic phase of the t–t’ Hubbard model. Phys. Rev. B 78, 041101 (2008).
doi: 10.1103/PhysRevB.78.041101
Luo, D. & Clark, B. K. Backflow transformations via neural networks for quantum many-body wave functions. Phys. Rev. Lett. 122, 226401 (2019).
pubmed: 31283262
doi: 10.1103/PhysRevLett.122.226401
Robledo Moreno, J., Carleo, G., Georges, A. & Stokes, J. Fermionic wave functions from neural-network constrained hidden states. Proc. Natl Acad. Sci. USA 119, e2122059119 (2022).
pubmed: 35921435
pmcid: 9371695
doi: 10.1073/pnas.2122059119
Lovato, A., Adams, C., Carleo, G. & Rocco, N. Hidden-nucleons neural-network quantum states for the nuclear many-body problem. Phys. Rev. Res. 4, 043178 (2022).
doi: 10.1103/PhysRevResearch.4.043178
Yang, Y. & Zhao, P. Deep-neural-network approach to solving the ab initio nuclear structure problem. Phys. Rev. C 107, 034320 (2023).
doi: 10.1103/PhysRevC.107.034320
Taddei, M., Ruggeri, M., Moroni, S. & Holzmann, M. Iterative backflow renormalization procedure for many-body ground-state wave functions of strongly interacting normal Fermi liquids. Phys. Rev. B 91, 115106 (2015).
doi: 10.1103/PhysRevB.91.115106
Ruggeri, M., Moroni, S. & Holzmann, M. Nonlinear network description for many-body quantum systems in continuous space. Phys. Rev. Lett. 120, 205302 (2018).
pubmed: 29864292
doi: 10.1103/PhysRevLett.120.205302
Chakravorty, S. J., Gwaltney, S. R. & Davidson, E. R. Ground-state correlation energies for atomic ions with to 18 electrons. Phys. Rev. A 44, 7071 (1991).
pubmed: 9905848
doi: 10.1103/PhysRevA.44.7071
Hermann, J., Schätzle, Z. & Noé, F. Deep-neural-network solution of the electronic Schrödinger equation. Nat. Chem. 12, 891–897 (2020).
pubmed: 32968231
doi: 10.1038/s41557-020-0544-y
Ma, A., Towler, M. D., Drummond, N. D. & Needs, R. J. Scheme for adding electron–nucleus cusps to Gaussian orbitals. J. Chem. Phys. 122, 224322 (2005).
pubmed: 15974683
doi: 10.1063/1.1940588
Schätzle, Z., Hermann, J. & Noé, F. Convergence to the fixed-node limit in deep variational Monte Carlo. J. Chem. Phys. 154, 124108 (2021).
pubmed: 33810658
doi: 10.1063/5.0032836
Pfau, D., Spencer, J. S., Matthews, A. G. D. G. & Foulkes, W. M. C. Ab initio solution of the many-electron Schrödinger equation with deep neural networks. Phys. Rev. Res. 2, 033429 (2020).
doi: 10.1103/PhysRevResearch.2.033429
Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. Preprint at http://arxiv.org/abs/1412.6980 (2015).
Martens, J. & Grosse, R. Optimizing neural networks with kronecker-factored approximate curvature. In Proceedings of the 32nd International Conference on Machine Learning 2408–2417 (PMLR, 2015).
Gerard, L., Scherbela, M., Marquetand, P. & Grohs, P. Gold-standard solutions to the Schrödinger equation using deep learning: how much physics do we need? In Advances in Neural Information Processing Systems, Vol. 35, 10282–10294 (Curran Associates, 2022).
von Glehn, I., Spencer, J. S. & Pfau, D. A self-attention ansatz for ab-initio quantum chemistry. In International Conference on Learning Representations (ICLR 2023) (OpenReview, 2023).
Scherbela, M., Reisenhofer, R., Gerard, L., Marquetand, P. & Grohs, P. Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks. Nat. Comput. Sci. 2, 331 (2022).
doi: 10.1038/s43588-022-00228-x
Yang, L., Hu, W. & Li, L. Scalable variational Monte Carlo with graph neural ansatz. Preprint at http://arxiv.org/abs/2011.12453 (2020).
Gao, N. & Günnemann, S. Ab-initio potential energy surfaces by pairing GNNs with neural wave functions. In International Conference on Learning Representations (ICLR 2022) (OpenReview, 2022).
Gao, N. & Günnemann, S. Sampling-free inference for ab-initio potential energy surface networks. In International Conference on Learning Representations (ICLR 2023) (OpenReview, 2023).
Feynman, R. P. Forces in molecules. Phys. Rev. 56, 340 (1939).
doi: 10.1103/PhysRev.56.340
Assaraf, R. & Caffarel, M. Zero-variance zero-bias principle for observables in quantum Monte Carlo: application to forces. J. Chem. Phys. 119, 10536–10552 (2003).
doi: 10.1063/1.1621615
Umrigar, C. Two aspects of quantum Monte Carlo: determination of accurate wavefunctions and determination of potential energy surfaces of molecules. Int. J. Quantum Chem. 36, 217–230 (1989).
doi: 10.1002/qua.560360826
Qian, Y., Fu, W., Ren, W. & Chen, J. Interatomic force from neural network based variational quantum Monte Carlo. J. Chem. Phys. 157, 164104 (2022).
pubmed: 36319420
doi: 10.1063/5.0112344
Pescia, G., Han, J., Lovato, A., Lu, J. & Carleo, G. Neural-network quantum states for periodic systems in continuous space. Phys. Rev. Res. 4, 023138 (2022).
doi: 10.1103/PhysRevResearch.4.023138
Wilson, M. et al. Neural network ansatz for periodic wave functions and the homogeneous electron gas. Phys. Rev. B 107, 235139 (2023).
doi: 10.1103/PhysRevB.107.235139
Cassella, G. et al. Discovering quantum phase transitions with fermionic neural networks. Phys. Rev. Lett. 130, 036401 (2023).
pubmed: 36763402
doi: 10.1103/PhysRevLett.130.036401
Li, X., Li, Z. & Chen, J. Ab initio calculation of real solids via neural network ansatz. Nat. Commun. 13, 7895 (2022).
pubmed: 36550157
pmcid: 9780243
doi: 10.1038/s41467-022-35627-1
Li, X., Fan, C., Ren, W. & Chen, J. Fermionic neural network with effective core potential. Phys. Rev. Res. 4, 013021 (2022).
doi: 10.1103/PhysRevResearch.4.013021
Needs, R. J., Towler, M. D., Drummond, N. D., López Ríos, P. & Trail, J. R. Variational and diffusion quantum Monte Carlo calculations with the CASINO code. J. Chem. Phys. 152, 154106 (2020).
pubmed: 32321255
doi: 10.1063/1.5144288
Shi, H. & Zhang, S. Some recent developments in auxiliary-field quantum Monte Carlo for real materials. J. Chem. Phys. 154, 024107 (2021).
pubmed: 33445908
doi: 10.1063/5.0031024
Wilson, M., Gao, N., Wudarski, F., Rieffel, E. & Tubman, N. M. Simulations of state-of-the-art fermionic neural network wave functions with diffusion Monte Carlo. Preprint at http://arxiv.org/abs/2103.12570 (2021).
Ren, W., Fu, W. & Chen, J. Towards the ground state of molecules via diffusion Monte Carlo on neural networks. Nat. Commun. 14, 1860 (2023).
pubmed: 37012248
pmcid: 10070323
doi: 10.1038/s41467-023-37609-3
Schautz, F. & Filippi, C. Optimized Jastrow–Slater wave functions for ground and excited states: application to the lowest states of ethene. J. Chem. Phys. 120, 10931 (2004).
pubmed: 15268123
doi: 10.1063/1.1752881
Dash, M., Feldt, J., Moroni, S., Scemama, A. & Filippi, C. Excited states with selected configuration interaction-quantum Monte Carlo: chemically accurate excitation energies and geometries. J. Chem. Theory Comput. 15, 4896 (2019).
pubmed: 31348645
pmcid: 6740157
doi: 10.1021/acs.jctc.9b00476
Zhao, L. & Neuscamman, E. An efficient variational principle for the direct optimization of excited states. J. Chem. Theory Comput. 12, 3436 (2016).
pubmed: 27379468
doi: 10.1021/acs.jctc.6b00508
Pathak, S., Busemeyer, B., Rodrigues, J. N. B. & Wagner, L. K. Excited states in variational Monte Carlo using a penalty method. J. Chem. Phys. 154, 034101 (2021).
pubmed: 33499613
doi: 10.1063/5.0030949
Entwistle, M., Schätzle, Z., Erdman, P. A., Hermann, J. & Noé, F. Electronic excited states in deep variational Monte Carlo. Nat. Commun. 14, 274 (2023).
pubmed: 36650151
pmcid: 9845370
doi: 10.1038/s41467-022-35534-5
Choo, K., Carleo, G., Regnault, N. & Neupert, T. Symmetries and many-body excitations with neural-network quantum states. Phys. Rev. Lett. 121, 167204 (2018).
pubmed: 30387658
doi: 10.1103/PhysRevLett.121.167204
Cuzzocrea, A., Scemama, A., Briels, W. J., Moroni, S. & Filippi, C. Variational principles in quantum Monte Carlo: the troubled story of variance minimization. J. Chem. Theory Comput. 16, 4203 (2020).
pubmed: 32419451
pmcid: 7365558
doi: 10.1021/acs.jctc.0c00147
Jordan, P. & Wigner, E. über das Paulische Äquivalenzverbot. Z. Phys. 47, 631 (1928).
doi: 10.1007/BF01331938
Bravyi, S. & Kitaev, A. Fermionic quantum computation. Ann. Phys. 298, 210–226 (2002).
doi: 10.1006/aphy.2002.6254
Sorella, S. Green function Monte Carlo with stochastic reconfiguration. Phys. Rev. Lett. 80, 4558–4561 (1998).
doi: 10.1103/PhysRevLett.80.4558
Choo, K., Mezzacapo, A. & Carleo, G. Fermionic neural-network states for ab-initio electronic structure. Nat. Commun. 11, 2368 (2020).
pubmed: 32398658
pmcid: 7217823
doi: 10.1038/s41467-020-15724-9
Yang, P.-J., Sugiyama, M., Tsuda, K. & Yanai, T. Artificial neural networks applied as molecular wave function solvers. J. Chem. Theory Comput. 16, 3513–3529 (2020).
pubmed: 32320233
doi: 10.1021/acs.jctc.9b01132
Torlai, G., Mazzola, G., Carleo, G. & Mezzacapo, A. Precise measurement of quantum observables with neural-network estimators. Phys. Rev. Res. 2, 022060 (2020).
doi: 10.1103/PhysRevResearch.2.022060
Iouchtchenko, D., Gonthier, J. F., Perdomo-Ortiz, A. & Melko, R. G. Neural network enhanced measurement efficiency for molecular groundstates. Mach. Learn. Sci. Technol. 4, 015016 (2023).
doi: 10.1088/2632-2153/acb4df
Glielmo, A., Rath, Y., Csányi, G., De Vita, A. & Booth, G. H. Gaussian process states: a data-driven representation of quantum many-body physics. Phys. Rev. X 10, 041026 (2020).
Del Re, G., Ladik, J. & Biczó, G. Self-consistent-field tight-binding treatment of polymers. I. Infinite three-dimensional case. Phys. Rev. 155, 997–1003 (1967).
doi: 10.1103/PhysRev.155.997
Yoshioka, N., Mizukami, W. & Nori, F. Solving quasiparticle band spectra of real solids using neural-network quantum states. Commun. Phys. 4, 1–8 (2021).
doi: 10.1038/s42005-021-00609-0
Barrett, T. D., Malyshev, A. & Lvovsky, A. I. Autoregressive neural-network wavefunctions for ab initio quantum chemistry. Nat. Mach. Intell. 4, 351 (2022).
doi: 10.1038/s42256-022-00461-z
Zhao, T., Stokes, J. & Veerapaneni, S. Scalable neural quantum states architecture for quantum chemistry. Mach. Learn. Sci. Technol. 4, 025034 (2023).
doi: 10.1088/2632-2153/acdb2f
Giner, E., Scemama, A. & Caffarel, M. Using perturbatively selected configuration interaction in quantum Monte Carlo calculations. Can. J. Chem. 91, 879–885 (2013).
doi: 10.1139/cjc-2013-0017
Holmes, A. A., Tubman, N. M. & Umrigar, C. Heat–bath configuration interaction: an efficient selected configuration interaction algorithm inspired by heat-bath sampling. J. Chem. Theory Comput. 12, 3674–3680 (2016).
pubmed: 27428771
doi: 10.1021/acs.jctc.6b00407
Sharma, S., Holmes, A. A., Jeanmairet, G., Alavi, A. & Umrigar, C. J. Semistochastic heat–bath configuration interaction method: selected configuration interaction with semistochastic perturbation theory. J. Chem. Theory Comput. 13, 1595–1604 (2017).
pubmed: 28263594
doi: 10.1021/acs.jctc.6b01028
Greer, J. Monte Carlo configuration interaction. J. Comput. Phys. 146, 181–202 (1998).
doi: 10.1006/jcph.1998.5953
Coe, J. P. Machine learning configuration interaction. J. Chem. Theory Comput. 14, 5739–5749 (2018).
pubmed: 30285426
doi: 10.1021/acs.jctc.8b00849
Goings, J. J., Hu, H., Yang, C. & Li, X. Reinforcement learning configuration interaction. J. Chem. Theory Comput. 17, 5482–5491 (2021).
pubmed: 34423637
doi: 10.1021/acs.jctc.1c00010
Pineda Flores, S. D. Chembot: a machine learning approach to selective configuration interaction. J. Chem. Theory Comput. 17, 4028 (2021).
pubmed: 34125549
doi: 10.1021/acs.jctc.1c00196
Nooijen, M., Shamasundar, K. & Mukherjee, D. Reflections on size-extensivity, size-consistency and generalized extensivity in many-body theory. Mol. Phys. 103, 2277–2298 (2005).
doi: 10.1080/00268970500083952
Hutter, M. On representing (anti)symmetric functions. Preprint at http://arxiv.org/abs/2007.15298 (2020).
Neuscamman, E. The Jastrow antisymmetric geminal power in Hilbert space: theory, benchmarking, and application to a novel transition state. J. Chem. Phys. 139, 194105 (2013).
pubmed: 24320314
doi: 10.1063/1.4829835
Sabzevari, I. & Sharma, S. Improved speed and scaling in orbital space variational Monte Carlo. J. Chem. Theory Comput. 14, 6276–6286 (2018).
pubmed: 30418769
doi: 10.1021/acs.jctc.8b00780
Rubenstein, B. Introduction to the variational monte carlo method in quantum chemistry and physics. In Variational Methods in Molecular Modeling 285–313 (Springer, 2017).
Toulouse, J., Assaraf, R. & Umrigar, C. J. Introduction to the variational and diffusion Monte Carlo methods. In Advances in Quantum Chemistry Vol. 73, 285–314 (Elsevier, 2016).
Amari, S. Natural gradient works efficiently in learning. Neural Comput. 10, 251–276 (1998).
doi: 10.1162/089976698300017746
Ay, N., Jost, J., Lê, H. V. & Schwachhöfer, L. Information Geometry. No. 64 in a Series of Modern Surveys in Mathematics (Springer, 2017).
Spencer, J. S., Pfau, D., Botev, A. & Foulkes, W. M. C. Better, faster fermionic neural networks. Preprint at http://arxiv.org/abs/2011.07125 (2020).