Eigenvector Continuation and Projection-Based Emulators

Abstract

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 article, we present the development, theory, and applications of eigenvector continuation and projection-based emulators. We introduce the basic concepts, discuss the underlying theory and convergence properties, and present recent applications for quantum systems and future prospects.

Final version to appear as colloquium article in Rev. Mod. Phys., 22 pages, 17 figures

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Cited by in corpus (25)

• Multiscale physics of atomic nuclei from first principles
• A Bayesian mixture model approach to quantifying the empirical nuclear saturation point
• Emulators for scarce and noisy data: application to auxiliary field diffusion Monte Carlo for the deuteron
• Lattice Effective Field Theory Simulations of Nuclei
• Emulators for Scarce and Noisy Data: Application to Auxiliary-Field Diffusion Monte Carlo for Neutron Matter
• From chiral EFT to perturbative QCD: a Bayesian model mixing approach to symmetric nuclear matter
• Towards scalable bound-to-resonance extrapolations for few- and many-body systems
• Greedy Emulators for Nuclear Two-Body Scattering
• Interpolating many-body wave functions for accelerated molecular dynamics on the near-exact electronic surface
• Global Framework for Emulation of Nuclear Calculations
• Non-Hermitian Quantum Mechanics Approach for Extracting and Emulating Continuum Physics Based on Bound-State-Like Calculations
• Non-Hermitian quantum mechanics approach for extracting and emulating continuum physics based on bound-state-like calculations: Detailed description
• Reduced Basis Method for Driven-Dissipative Quantum Systems
• Controlled Gate Networks: Theory and Application to Eigenvalue Estimation
• Active learning emulators for nuclear two-body scattering in momentum space
• An Efficient Learning Method to Connect Observables
• Cheaper and more noise-resilient quantum state preparation using eigenvector continuation
• Ab initio study of the neutron and Fermi polarons on the lattice
• Recent applications of the subtracted second RPA method
• Hartree-Fock emulators for nuclei: Application to charge radii of ${}^{48,52}$Ca
• Linear Foundation Model for Quantum Embedding: Data-Driven Compression of the Ghost Gutzwiller Variational Space
• Chiral interactions and superfluidity in the calcium isotopic chain
• Constraining Hamiltonians from chiral effective field theory with neutron-star data
• Efficient emulation of nuclear ground states with neural-network variational Monte Carlo and eigenvector continuation
• Conformal prediction for uncertainties in nucleon-nucleon scattering