Electron correlation in semiconductors and insulators via symbolic regression

Abstract

Predicting quasiparticle energies in materials requires expensive numerical evaluations of the electron self-energy. This limits calculations to ordered systems with small unit cells. Here, using symbolic regression, we show that the GW self-energy can be accurately approximated with compact analytical functions of physically motivated Kohn-Sham descriptors. These expressions can be learned from a single GW calculation in the ordered phase and remain accurate under symmetry breaking induced by quantum and thermal fluctuations, elastic deformations, and amorphous disorder. This development enables routine GW calculations of complex materials with thousands of atoms at a computational cost comparable to semi-local density functional theory. We demonstrate the accuracy of this approach for covalent semiconductors, ionic insulators, and two-dimensional materials. These results establish symbolic regression as a viable route to predictive, interpretable, and transferable many-body electronic structure models.

Main manuscript and supplemental material

References in corpus (34)

• Advanced capabilities for materials modelling with Quantum ESPRESSO
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Optimized norm-conserving Vanderbilt pseudopotentials
• The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table
• Quantum ESPRESSO toward the exascale
• Wannier90 as a community code: new features and applications
• Electron-phonon interactions from first principles
• BerkeleyGW: A Massively Parallel Computer Package for the Calculation of the Quasiparticle and Optical Properties of Materials and Nanostructures
• Quasiparticle Self-Consistent GW Theory
• SISSO: a compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates
• Nearsightedness of Electronic Matter
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials
• Density functional perturbation theory for gated two-dimensional heterostructures: Theoretical developments and application to flexural phonons in graphene
• Interpretable Scientific Discovery with Symbolic Regression: A Review
• Symbolic Regression in Materials Science
• Strain-Enhanced Mobility of Monolayer MoS2
• Electron-Phonon Interaction in Tetrahedral Semiconductors
• Towards GW Calculations on Thousands of Atoms
• Quasiparticle Effects in the Bulk and Surface-State Bands of Bi2Se3 and Bi2Te3 Topological Insulators
• Band widths and gaps from the Tran-Blaha functional : Comparison with many-body perturbation theory
• Electron-Phonon Coupling from $\text{Ab Initio}$ Linear-Response Theory within the $GW$ Method: Correlation-Enhanced Interactions and Superconductivity in Ba${}_{1-x}$K${}_x$BiO${}_3$
• Theory of the special displacement method for electronic structure calculations at finite temperature
• Cubic-scaling all-electron GW calculations with a separable density-fitting space-time approach
• Correlation effects on electron-phonon coupling in semiconductors: many-body theory along thermal lines
• Representing individual electronic states for machine learning GW band structures of 2D materials
• Swift $GW$ beyond $10,000$ electrons using fractured stochastic orbitals
• Physically inspired deep learning of molecular excitations and photoemission spectra
• Exploring approximations to the GW self-energy ionic gradients
• Evolving symbolic density functionals
• Theory of temperature dependent phonon-renormalized properties
• Unified Deep Learning Framework for Many-Body Quantum Chemistry via Green's Functions
• Efficient Full-frequency GW Calculations using a Lanczos Method
• Equivariant neural network for Green's functions of molecules and materials