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

References in corpus (41)

• Coupled-cluster computations of atomic nuclei
• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Ab initio predictions link the neutron skin of ${}^{208}$Pb to nuclear forces
• Eigenvector continuation with subspace learning
• Global sensitivity analysis of bulk properties of an atomic nucleus
• Nuclear binding near a quantum phase transition
• Eigenvector Continuation as an Efficient and Accurate Emulator for Uncertainty Quantification
• Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States
• Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables
• Deep learning-based reduced order models in cardiac electrophysiology
• What is ab initio in nuclear theory?
• Multi-reference many-body perturbation theory for nuclei III -- Ab initio calculations at second order in PGCM-PT
• Data driven approximation of parametrized PDEs by Reduced Basis and Neural Networks
• Efficient emulators for scattering using eigenvector continuation
• Improved many-body expansions from eigenvector continuation
• $\mu$TRISTAN
• Signatures of few-body resonances in finite volume
• Model reduction methods for nuclear emulators
• Fast & accurate emulation of two-body scattering observables without wave functions
• Convergence of Eigenvector Continuation
• Fast emulation of quantum three-body scattering
• Generalizing the calculable $R$-matrix theory and eigenvector continuation to the incoming wave boundary condition
• Bogoliubov many-body perturbation theory under constraint
• Calculation of three-body resonances using slow-variable discretization coupled with complex absorbing potential
• Fast & rigorous predictions for $A=6$ nuclei with Bayesian posterior sampling
• Self-learning Emulators and Eigenvector Continuation
• Eigenvector continuation for emulating and extrapolating two-body resonances
• Excited states from eigenvector continuation: the anharmonic oscillator
• Emulating \emph{ab initio} computations of infinite nucleonic matter
• Surrogate models for quantum spin systems based on reduced order modeling
• Inference of the low-energy constants in $\Delta$-full chiral effective field theory including a correlated truncation error
• Volume extrapolation via eigenvector continuation
• Wave-function-based emulation for nucleon-nucleon scattering in momentum space
• Nuclear-matter saturation and symmetry energy within $\Delta$--full chiral effective field theory
• Reduced basis emulation of pairing in finite systems
• Reduced basis surrogates for quantum spin systems based on tensor networks
• Quantum Eigenvector Continuation for Chemistry Applications
• Floating block method for quantum Monte Carlo simulations
• Trimmed Sampling Algorithm for the Noisy Generalized Eigenvalue Problem
• Fundamental limitations of the eigenvalue continuation approach

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