Self-learning Emulators and Eigenvector Continuation

Abstract

Emulators that can bypass computationally expensive scientific calculations with high accuracy and speed can enable new studies of fundamental science as well as more potential applications. In this work we discuss solving a system of constraint equations efficiently using a self-learning emulator. A self-learning emulator is an active learning protocol that can be used with any emulator that faithfully reproduces the exact solution at selected training points. The key ingredient is a fast estimate of the emulator error that becomes progressively more accurate as the emulator is improved, and the accuracy of the error estimate can be corrected using machine learning. We illustrate with three examples. The first uses cubic spline interpolation to find the solution of a transcendental equation with variable coefficients. The second example compares a spline emulator and a reduced basis method emulator to find solutions of a parameterized differential equation. The third example uses eigenvector continuation to find the eigenvectors and eigenvalues of a large Hamiltonian matrix that depends on several control parameters.

6 + 5 pages (main + supplemental), 5 + 7 figures (main + supplemental), additional discussion, references, and examples added

References in corpus (6)

• Global sensitivity analysis of bulk properties of an atomic nucleus
• Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables
• Fast & accurate emulation of two-body scattering observables without wave functions
• Generalizing the calculable $R$-matrix theory and eigenvector continuation to the incoming wave boundary condition
• Precision benchmark calculations for four particles at unitarity
• Constructing approximate shell-model wavefunctions by eigenvector continuation

Cited by in corpus (17)

• Machine Learning in Nuclear Physics
• Model reduction methods for nuclear emulators
• Eigenvector Continuation and Projection-Based Emulators
• Training and Projecting: A Reduced Basis Method Emulator for Many-Body Physics
• Emulating \emph{ab initio} computations of infinite nucleonic matter
• Mapping out the thermodynamic stability of a QCD equation of state with a critical point using active learning
• Volume extrapolation via eigenvector continuation
• Reduced basis emulation of pairing in finite systems
• Reduced basis surrogates for quantum spin systems based on tensor networks
• Floating block method for quantum Monte Carlo simulations
• Greedy Emulators for Nuclear Two-Body Scattering
• Neural Network Emulation of Flow in Heavy-Ion Collisions at Intermediate Energies
• IMSRG-Net: A machine learning-based solver for In-Medium Similarity Renormalization Group
• Non-Hermitian quantum mechanics approach for extracting and emulating continuum physics based on bound-state-like calculations: Detailed description
• Non-Hermitian Quantum Mechanics Approach for Extracting and Emulating Continuum Physics Based on Bound-State-Like Calculations
• Reduced Basis Method for Driven-Dissipative Quantum Systems
• Active learning emulators for nuclear two-body scattering in momentum space