Insights into one-body density matrices using deep learning

Abstract

The one-body reduced density matrix (1-RDM) of a many-body system at zero temperature gives direct access to many observables, such as the charge density, kinetic energy and occupation numbers. It would be desirable to express it as a simple functional of the density or of other local observables, but to date satisfactory approximations have not yet been found. Deep learning is the state-of the art approach to perform high dimensional regressions and classification tasks, and is becoming widely used in the condensed matter community to develop increasingly accurate density functionals. Autoencoders are deep learning models that perform efficient dimensionality reduction, allowing the distillation of data to its fundamental features needed to represent it. By training autoencoders on a large data-set of 1-RDMs from exactly solvable real-space model systems, and performing principal component analysis, the machine learns to what extent the data can be compressed and hence how it is constrained. We gain insight into these machine learned constraints and employ them to inform approximations to the 1-RDM as a functional of the charge density. We exploit known physical properties of the 1-RDM in the simplest possible cases to perform feature engineering, where we inform the structure of the models from known mathematical relations, allowing us to integrate existing understanding into the machine learning methods. By comparing various deep learning approaches we gain insight into what physical features of the density matrix are most amenable to machine learning, utilising both known and learned characteristics.

15 pages, 11 figures

References in corpus (25)

• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• Machine learning and the physical sciences
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• By-passing the Kohn-Sham equations with machine learning
• Finding Density Functionals with Machine Learning
• A natural orbital functional for the many-electron problem
• Reduced Density Matrix Functional for Many-Electron Systems
• Deep learning and the Schrödinger equation
• Global Method for Electron Correlation
• Deep Learning and Density Functional Theory
• Pure density functional for strong correlations and the thermodynamic limit from machine learning
• Neural-network Kohn-Sham exchange-correlation potential and its out-of-training transferability
• Relating the pure and ensemble density matrix functional
• Performance of one-body reduced density matrix functionals for the homogeneous electron gas
• How is the derivative discontinuity related to steps in the exact Kohn-Sham potential?
• Exact time-dependent density-functional potentials for strongly correlated tunneling electrons
• Origin of static and dynamic steps in exact Kohn-Sham potentials
• Landscape of an exact energy functional
• Accuracy of electron densities obtained via Koopmans-compliant hybrid functionals
• The role of electron localization in density functionals
• Advantageous nearsightedness of many-body perturbation theory contrasted with Kohn-Sham density functional theory
• Approximate energy functionals for one-body reduced density matrix functional theory from many-body perturbation theory
• $GW$ self-screening error and its correction using a local density functional
• Accurate real-time evolution of electron densities and ground-state properties from generalized Kohn-Sham theory
• Metrics for two electron random potential systems

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• Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer