Colloquium: Eigenvector continuation and projection-based emulators

Duguet, Thomas; Ekström, Andreas; Furnstahl, Richard J.; König, Sebastian; Lee, Dean

doi:10.1103/revmodphys.96.031002

Colloquium: Eigenvector continuation and projection-based emulators

Journal Article · Wed Aug 14 00:00:00 EDT 2024 · Reviews of Modern Physics

DOI:https://doi.org/10.1103/revmodphys.96.031002· OSTI ID:2477753

Duguet, Thomas ^[1]; Ekström, Andreas ^[2]; Furnstahl, Richard J. ^[3]; König, Sebastian ^[4]; ^[5]

Université Paris-Saclay, Gif-sur-Yvette (France); KU Leuven (Belgium)
Chalmers University of Technology, Göteborg (Sweden)
The Ohio State University, Columbus, OH (United States)
North Carolina State University, Raleigh, NC (United States)
Michigan State University, East Lansing, MI (United States)

Eigenvector continuation is a computational method for parametric eigenvalue problems that uses subspace projection with a basis derived from eigenvector snapshots from different parameter sets. It is part of a broader class of subspace-projection techniques called reduced-basis methods. In this Colloquium, the development, theory, and applications of eigenvector continuation and projection-based emulators are presented. In conclusion, the basic concepts are introduced, the underlying theory and convergence properties are discussed, and recent applications for quantum systems and future prospects are presented.

View Accepted Manuscript (DOE)

Research Organization:: Michigan State University, East Lansing, MI (United States)

Sponsoring Organization:: European Union Horizon 2020 research and innovation program; Swedish Research Council; U.S. National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0013365; SC0013617; SC0023175; SC0023658; SC0024509; SC0024520; SC0024586; SC0024622

OSTI ID:: 2477753

Alternate ID(s):: OSTI ID: 2474640

Journal Information:: Reviews of Modern Physics, Journal Name: Reviews of Modern Physics Journal Issue: 3 Vol. 96; ISSN 0034-6861

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (87)

The Mathematical Theory of Finite Element Methods Brenner, Susanne C.; Scott, L. Ridgway Texts in Applied Mathematics https://doi.org/10.1007/978-0-387-75934-0	book	January 2008
Reduced Basis Methods for Partial Differential Equations Quarteroni, Alfio; Manzoni, Andrea; Negri, Federico UNITEXT https://doi.org/10.1007/978-3-319-15431-2	book	January 2016
Certified Reduced Basis Methods for Parametrized Partial Differential Equations Hesthaven, Jan S.; Rozza, Gianluigi; Stamm, Benjamin SpringerBriefs in Mathematics https://doi.org/10.1007/978-3-319-22470-1	book	January 2016
A mathematical foundation for discretisation techniques in the generator coordinate method Broeckhove, J.; Deumens, E. Zeitschrift f�r Physik A Atoms and Nuclei, Vol. 292, Issue 3 https://doi.org/10.1007/BF01547468	journal	September 1979
Nuclear Forces for Precision Nuclear Physics: A Collection of Perspectives Tews, Ingo; Davoudi, Zohreh; Ekström, Andreas Few-Body Systems, Vol. 63, Issue 4 https://doi.org/10.1007/s00601-022-01749-x	journal	September 2022
A Reduced Order Model Approach to Inverse Scattering in Lossy Layered Media Borcea, Liliana; Druskin, Vladimir; Zimmerling, Jörn Journal of Scientific Computing, Vol. 89, Issue 1 https://doi.org/10.1007/s10915-021-01616-7	journal	August 2021
The generator coordinate theory of collective motion Brink, D. M.; Weiguny, A. Nuclear Physics A, Vol. 120, Issue 1 https://doi.org/10.1016/0375-9474(68)90059-6	journal	November 1968
Signatures of unstable particles in finite volume Lüscher, Martin Nuclear Physics B, Vol. 364, Issue 1 https://doi.org/10.1016/0550-3213(91)90584-K	journal	October 1991
Resonance scattering phase shifts on a non-rest-frame lattice Rummukainen, K.; Gottlieb, Steven Nuclear Physics B, Vol. 450, Issue 1-2 https://doi.org/10.1016/0550-3213(95)00313-H	journal	September 1995
Identification of resonance parameters from the finite volume energy spectrum Wiese, U. -J. Nuclear Physics B - Proceedings Supplements, Vol. 9 https://doi.org/10.1016/0920-5632(89)90171-0	journal	June 1989
Monte Carlo shell model for atomic nuclei Otsuka, T.; Honma, M.; Mizusaki, T. Progress in Particle and Nuclear Physics, Vol. 47, Issue 1 https://doi.org/10.1016/S0146-6410(01)00157-0	journal	January 2001
Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems Machiels, Luc; Maday, Yvon; Oliveira, Ivan B. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Vol. 331, Issue 2 https://doi.org/10.1016/S0764-4442(00)00270-6	journal	July 2000
Bogoliubov many-body perturbation theory under constraint Demol, P.; Frosini, M.; Tichai, A. Annals of Physics, Vol. 424 https://doi.org/10.1016/j.aop.2020.168358	journal	January 2021
On the stability of the reduced basis method for Stokes equations in parametrized domains Rozza, Gianluigi; Veroy, Karen Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 7 https://doi.org/10.1016/j.cma.2006.09.005	journal	January 2007
Data driven approximation of parametrized PDEs by reduced basis and neural networks Dal Santo, Niccolò; Deparis, Simone; Pegolotti, Luca Journal of Computational Physics, Vol. 416 https://doi.org/10.1016/j.jcp.2020.109550	journal	September 2020
Physics-informed machine learning for reduced-order modeling of nonlinear problems Chen, Wenqian; Wang, Qian; Hesthaven, Jan S. Journal of Computational Physics, Vol. 446 https://doi.org/10.1016/j.jcp.2021.110666	journal	December 2021
Hartree–Fock many-body perturbation theory for nuclear ground-states Tichai, Alexander; Langhammer, Joachim; Binder, Sven Physics Letters B, Vol. 756 https://doi.org/10.1016/j.physletb.2016.03.029	journal	May 2016
Efficient emulators for scattering using eigenvector continuation Furnstahl, R. J.; Garcia, A. J.; Millican, P. J. Physics Letters B, Vol. 809 https://doi.org/10.1016/j.physletb.2020.135719	journal	October 2020
Eigenvector continuation as an efficient and accurate emulator for uncertainty quantification König, S.; Ekström, A.; Hebeler, K. Physics Letters B, Vol. 810 https://doi.org/10.1016/j.physletb.2020.135814	journal	November 2020
Fast & accurate emulation of two-body scattering observables without wave functions Melendez, J. A.; Drischler, C.; Garcia, A. J. Physics Letters B, Vol. 821 https://doi.org/10.1016/j.physletb.2021.136608	journal	October 2021
Toward emulating nuclear reactions using eigenvector continuation Drischler, C.; Quinonez, M.; Giuliani, P. G. Physics Letters B, Vol. 823 https://doi.org/10.1016/j.physletb.2021.136777	journal	December 2021
Excited states from eigenvector continuation: The anharmonic oscillator Companys Franzke, M.; Tichai, A.; Hebeler, K. Physics Letters B, Vol. 830 https://doi.org/10.1016/j.physletb.2022.137101	journal	July 2022
Data-Driven Science and Engineering Brunton, Steven L.; Kutz, J. Nathan https://doi.org/10.1017/9781108380690	book	February 2019
Many – Body Methods in Chemistry and Physics Shavitt, Isaiah; Bartlett, Rodney J. https://doi.org/10.1017/CBO9780511596834	book	January 2009
Non-Hermitian Quantum Mechanics Moiseyev, Nimrod https://doi.org/10.1017/CBO9780511976186	book	May 2011
Ab initio predictions link the neutron skin of 208Pb to nuclear forces Hu, Baishan; Jiang, Weiguang; Miyagi, Takayuki Nature Physics, Vol. 18, Issue 10 https://doi.org/10.1038/s41567-022-01715-8	journal	August 2022
First observation of 28O Kondo, Y.; Achouri, N. L.; Falou, H. Al Nature, Vol. 620, Issue 7976 https://doi.org/10.1038/s41586-023-06352-6	journal	August 2023
Reduced basis approximation anda posteriorierror estimates for parametrized elliptic eigenvalue problems Fumagalli, Ivan; Manzoni, Andrea; Parolini, Nicola ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 50, Issue 6 https://doi.org/10.1051/m2an/2016009	journal	October 2016
Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems Horger, Thomas; Wohlmuth, Barbara; Dickopf, Thomas ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 51, Issue 2 https://doi.org/10.1051/m2an/2016025	journal	February 2017
Hartree–Fock solutions as a quasidiabatic basis for nonorthogonal configuration interaction Thom, Alex J. W.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 131, Issue 12 https://doi.org/10.1063/1.3236841	journal	September 2009
Diameters of sets in Function Spaces and the Theory of best Approximations Tikhomirov, V. M. Russian Mathematical Surveys, Vol. 15, Issue 3 https://doi.org/10.1070/rm1960v015n03abeh004093	journal	June 1960
Resonances in Few-body Systems Afnan, Ir Australian Journal of Physics, Vol. 44, Issue 3 https://doi.org/10.1071/PH910201	journal	January 1991
Resonance properties of complex-rotated hamiltonians Moiseyev, N.; Certain, P. R.; Weinhold, F. Molecular Physics, Vol. 36, Issue 6 https://doi.org/10.1080/00268977800102631	journal	December 1978
Reduced Basis Eigenvalue Solutions for Damaged Structures∗ Aktas, Engin; Moses, Fred Mechanics of Structures and Machines, Vol. 26, Issue 1 https://doi.org/10.1080/08905459808945420	journal	January 1998
Reduced Basis Method for Optimal Control of Unsteady Viscous Flows Ito, K.; Ravindran, S. S. International Journal of Computational Fluid Dynamics, Vol. 15, Issue 2 https://doi.org/10.1080/10618560108970021	journal	October 2001
Coupled-cluster computations of atomic nuclei Hagen, G.; Papenbrock, T.; Hjorth-Jensen, M. Reports on Progress in Physics, Vol. 77, Issue 9 https://doi.org/10.1088/0034-4885/77/9/096302	journal	September 2014
Model reduction methods for nuclear emulators Melendez, J. A.; Drischler, C.; Furnstahl, R. J. Journal of Physics G: Nuclear and Particle Physics, Vol. 49, Issue 10 https://doi.org/10.1088/1361-6471/ac83dd	journal	September 2022
Quantum eigenvector continuation for chemistry applications Mejuto-Zaera, Carlos; Kemper, Alexander F. Electronic Structure, Vol. 5, Issue 4 https://doi.org/10.1088/2516-1075/ad018f	journal	November 2023
μTristan Hamada, Yu; Kitano, Ryuichiro; Matsudo, Ryutaro Progress of Theoretical and Experimental Physics, Vol. 2022, Issue 5 https://doi.org/10.1093/ptep/ptac059	journal	March 2022
New-generation Monte Carlo shell model for the K computer era Shimizu, Noritaka; Abe, Takashi; Tsunoda, Yusuke Progress of Theoretical and Experimental Physics, Vol. 2012, Issue 1 https://doi.org/10.1093/ptep/pts012	journal	January 2012
Collective Motions in Nuclei by the Method of Generator Coordinates Griffin, James J.; Wheeler, John A. Physical Review, Vol. 108, Issue 2 https://doi.org/10.1103/PhysRev.108.311	journal	October 1957
Variational Methods in Nuclear Collision Problems Kohn, W. Physical Review, Vol. 74, Issue 12 https://doi.org/10.1103/PhysRev.74.1763	journal	December 1948
Calculation of three-body resonances using slow-variable discretization coupled with a complex absorbing potential Blandon, Juan; Kokoouline, Viatcheslav; Masnou-Seeuws, Françoise Physical Review A, Vol. 75, Issue 4 https://doi.org/10.1103/PhysRevA.75.042508	journal	April 2007
Reduced basis emulation of pairing in finite systems Baran, V. V.; Nichita, D. R. Physical Review B, Vol. 107, Issue 14 https://doi.org/10.1103/PhysRevB.107.144503	journal	April 2023
Improved many-body expansions from eigenvector continuation Demol, P.; Duguet, T.; Ekström, A. Physical Review C, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevC.101.041302	journal	April 2020
Generalizing the calculable R -matrix theory and eigenvector continuation to the incoming-wave boundary condition Bai, Dong; Ren, Zhongzhou Physical Review C, Vol. 103, Issue 1 https://doi.org/10.1103/PhysRevC.103.014612	journal	January 2021
Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables Wesolowski, S.; Svensson, I.; Ekström, A. Physical Review C, Vol. 104, Issue 6 https://doi.org/10.1103/PhysRevC.104.064001	journal	December 2021
Bayesian predictions for A=6 nuclei using eigenvector continuation emulators Djärv, T.; Ekström, A.; Forssén, C. Physical Review C, Vol. 105, Issue 1 https://doi.org/10.1103/PhysRevC.105.014005	journal	January 2022
Fast emulation of quantum three-body scattering Zhang, Xilin; Furnstahl, R. J. Physical Review C, Vol. 105, Issue 6 https://doi.org/10.1103/PhysRevC.105.064004	journal	June 2022
Volume extrapolation via eigenvector continuation Yapa, Nuwan; König, Sebastian Physical Review C, Vol. 106, Issue 1 https://doi.org/10.1103/PhysRevC.106.014309	journal	July 2022
Fundamental limitations of the eigenvalue continuation approach Sowiński, Tomasz; Garcia-March, Miguel A. Physical Review C, Vol. 106, Issue 2 https://doi.org/10.1103/PhysRevC.106.024002	journal	August 2022
New extensions of eigenvector continuation R -matrix theory based on analyticity in momentum and angular momentum Bai, Dong Physical Review C, Vol. 106, Issue 2 https://doi.org/10.1103/PhysRevC.106.024611	journal	August 2022
Training and projecting: A reduced basis method emulator for many-body physics Bonilla, Edgard; Giuliani, Pablo; Godbey, Kyle Physical Review C, Vol. 106, Issue 5 https://doi.org/10.1103/PhysRevC.106.054322	journal	November 2022
Wave-function-based emulation for nucleon-nucleon scattering in momentum space Garcia, A. J.; Drischler, C.; Furnstahl, R. J. Physical Review C, Vol. 107, Issue 5 https://doi.org/10.1103/PhysRevC.107.054001	journal	May 2023
Eigenvector continuation for emulating and extrapolating two-body resonances Yapa, Nuwan; Fossez, Kévin; König, Sebastian Physical Review C, Vol. 107, Issue 6 https://doi.org/10.1103/PhysRevC.107.064316	journal	June 2023
Eigenvector continuation for the pairing Hamiltonian Companys Franzke, M.; Tichai, A.; Hebeler, K. Physical Review C, Vol. 109, Issue 2 https://doi.org/10.1103/PhysRevC.109.024311	journal	February 2024
ROSE: A reduced-order scattering emulator for optical models Odell, D.; Giuliani, P.; Beyer, K. Physical Review C, Vol. 109, Issue 4 https://doi.org/10.1103/PhysRevC.109.044612	journal	April 2024
Inference of the low-energy constants in Δ -full chiral effective field theory including a correlated truncation error Svensson, Isak; Ekström, Andreas; Forssén, Christian Physical Review C, Vol. 109, Issue 6 https://doi.org/10.1103/PhysRevC.109.064003	journal	June 2024
Emulating ab initio computations of infinite nucleonic matter Jiang, W. G.; Forssén, C.; Djärv, T. Physical Review C, Vol. 109, Issue 6 https://doi.org/10.1103/PhysRevC.109.064314	journal	June 2024
Nuclear-matter saturation and symmetry energy within Δ -full chiral effective field theory Jiang, W. G.; Forssén, C.; Djärv, T. Physical Review C, Vol. 109, Issue 6 https://doi.org/10.1103/PhysRevC.109.L061302	journal	June 2024
Properties of Griffin-Hill-Wheeler spaces de Toledo Piza, A. F. R.; de Passos, E. J. V.; Galetti, D. Physical Review C, Vol. 15, Issue 4 https://doi.org/10.1103/PhysRevC.15.1477	journal	April 1977
New “USD” Hamiltonians for the sd shell Brown, B. Alex; Richter, W. A. Physical Review C, Vol. 74, Issue 3 https://doi.org/10.1103/PhysRevC.74.034315	journal	September 2006
Signatures of few-body resonances in finite volume Klos, P.; König, S.; Hammer, H. -W. Physical Review C, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevC.98.034004	journal	September 2018
Surrogate models for quantum spin systems based on reduced-order modeling Herbst, Michael F.; Stamm, Benjamin; Wessel, Stefan Physical Review E, Vol. 105, Issue 4 https://doi.org/10.1103/PhysRevE.105.045303	journal	April 2022
Reduced basis surrogates for quantum spin systems based on tensor networks Brehmer, Paul; Herbst, Michael F.; Wessel, Stefan Physical Review E, Vol. 108, Issue 2 https://doi.org/10.1103/PhysRevE.108.025306	journal	August 2023
Nuclear Binding Near a Quantum Phase Transition Elhatisari, Serdar; Li, Ning; Rokash, Alexander Physical Review Letters, Vol. 117, Issue 13 https://doi.org/10.1103/PhysRevLett.117.132501	journal	September 2016
Eigenvector Continuation with Subspace Learning Frame, Dillon; He, Rongzheng; Ipsen, Ilse Physical Review Letters, Vol. 121, Issue 3 https://doi.org/10.1103/PhysRevLett.121.032501	journal	July 2018
Global Sensitivity Analysis of Bulk Properties of an Atomic Nucleus Ekström, Andreas; Hagen, Gaute Physical Review Letters, Vol. 123, Issue 25 https://doi.org/10.1103/PhysRevLett.123.252501	journal	December 2019
Convergence of Eigenvector Continuation Sarkar, Avik; Lee, Dean Physical Review Letters, Vol. 126, Issue 3 https://doi.org/10.1103/PhysRevLett.126.032501	journal	January 2021
Floating Block Method for Quantum Monte Carlo Simulations Sarkar, Avik; Lee, Dean; Meißner, Ulf-G. Physical Review Letters, Vol. 131, Issue 24 https://doi.org/10.1103/PhysRevLett.131.242503	journal	December 2023
Self-learning emulators and eigenvector continuation Sarkar, Avik; Lee, Dean Physical Review Research, Vol. 4, Issue 2 https://doi.org/10.1103/PhysRevResearch.4.023214	journal	June 2022
Trimmed sampling algorithm for the noisy generalized eigenvalue problem Hicks, Caleb; Lee, Dean Physical Review Research, Vol. 5, Issue 2 https://doi.org/10.1103/PhysRevResearch.5.L022001	journal	April 2023
Coupled-cluster theory in quantum chemistry Bartlett, Rodney J.; Musiał, Monika Reviews of Modern Physics, Vol. 79, Issue 1 https://doi.org/10.1103/RevModPhys.79.291	journal	February 2007
Numerical Methods for Large Eigenvalue Problems Saad, Yousef https://doi.org/10.1137/1.9781611970739	book	January 2011
A Reduced Order Modeling Technique to Study Bifurcating Phenomena: Application to the Gross--Pitaevskii Equation Pichi, Federico; Quaini, Annalisa; Rozza, Gianluigi SIAM Journal on Scientific Computing, Vol. 42, Issue 5 https://doi.org/10.1137/20M1313106	journal	January 2020
Multi-reference many-body perturbation theory for nuclei: I. Novel PGCM-PT formalism Frosini, M.; Duguet, T.; Ebran, J. -P. The European Physical Journal A, Vol. 58, Issue 4 https://doi.org/10.1140/epja/s10050-022-00692-z	journal	April 2022
Multi-reference many-body perturbation theory for nuclei: III. Ab initio calculations at second order in PGCM-PT Frosini, M.; Duguet, T.; Ebran, J. -P. The European Physical Journal A, Vol. 58, Issue 4 https://doi.org/10.1140/epja/s10050-022-00694-x	journal	April 2022
Deep learning-based reduced order models in cardiac electrophysiology Fresca, Stefania; Manzoni, Andrea; Dedè, Luca PLOS ONE, Vol. 15, Issue 10 https://doi.org/10.1371/journal.pone.0239416	journal	October 2020
A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code McKay, M. D.; Beckman, R. J.; Conover, W. J. Technometrics, Vol. 21, Issue 2 https://doi.org/10.2307/1268522	journal	May 1979
Uber Die Beste Annaherung Von Funktionen Einer Gegebenen Funktionenklasse Kolmogoroff, A. The Annals of Mathematics, Vol. 37, Issue 1 https://doi.org/10.2307/1968691	journal	January 1936
Improved First-Order Approximation of Eigenvalues and Eigenvectors Nair, Prasanth B.; Keane, Andrew J.; Langley, Robin S. AIAA Journal, Vol. 36, Issue 9 https://doi.org/10.2514/2.578	journal	September 1998
Many-Body Perturbation Theories for Finite Nuclei Tichai, Alexander; Roth, Robert; Duguet, Thomas Frontiers in Physics, Vol. 8 https://doi.org/10.3389/fphy.2020.00164	journal	June 2020
A Guided Tour of ab initio Nuclear Many-Body Theory Hergert, Heiko Frontiers in Physics, Vol. 8 https://doi.org/10.3389/fphy.2020.00379	journal	October 2020
Bayes goes fast: Uncertainty quantification for a covariant energy density functional emulated by the reduced basis method Giuliani, Pablo; Godbey, Kyle; Bonilla, Edgard Frontiers in Physics, Vol. 10 https://doi.org/10.3389/fphy.2022.1054524	journal	January 2023
BUQEYE guide to projection-based emulators in nuclear physics Drischler, C.; Melendez, J. A.; Furnstahl, R. J. Frontiers in Physics, Vol. 10 https://doi.org/10.3389/fphy.2022.1092931	journal	February 2023
Ab initio symmetry-adapted emulator for studying emergent collectivity and clustering in nuclei Becker, K. S.; Launey, K. D.; Ekström, A. Frontiers in Physics, Vol. 11 https://doi.org/10.3389/fphy.2023.1064601	journal	March 2023
What is ab initio in nuclear theory? Ekström, A.; Forssén, C.; Hagen, G. Frontiers in Physics, Vol. 11 https://doi.org/10.3389/fphy.2023.1129094	journal	February 2023

Similar Records

Convergence of Eigenvector Continuation

Journal Article · Wed Jan 20 19:00:00 EST 2021 · Physical Review Letters · OSTI ID:1852672

Eigenvector Continuation with Subspace Learning

Journal Article · Mon Jul 16 20:00:00 EDT 2018 · Physical Review Letters · OSTI ID:1541342

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Ab initio calculations
Few-body systems
Many-body techniques
Nuclear many-body theory
Quantum Monte Carlo
Shell model

Colloquium: Eigenvector continuation and projection-based emulators

Citation Formats

References (87)

Similar Records

Related Subjects