Design and Analysis of Machine Learning Exchange-Correlation Functionals via Rotationally Invariant Convolutional Descriptors

Abstract

In this work we explore the potential of a new data-driven approach to the design of exchange-correlation (XC) functionals. The approach, inspired by convolutional filters in computer vision and surrogate functions from optimization, utilizes convolutions of the electron density to form a feature space to represent local electronic environments and neural networks to map the features to the exchange-correlation energy density. These features are orbital free, and provide a systematic route to including information at various length scales. This work shows that convolutional descriptors are theoretically capable of an exact representation of the electron density, and proposes Maxwell-Cartesian spherical harmonic kernels as a class of rotationally invariant descriptors for the construction of machine-learned functionals. The approach is demonstrated using data from the B3LYP functional on a number of small-molecules containing C, H, O, and N along with a neural network regression model. The machine-learned functionals are compared to standard physical approximations and the accuracy is assessed for the absolute energy of each molecular system as well as formation energies. The results indicate that it is possible to reproduce B3LYP formation energies to within chemical accuracy using orbital-free descriptors with a spatial extent of 0.2 A. The findings provide empirical insight into the spatial range of electron exchange, and suggest that the combination of convolutional descriptors and machine-learning regression models is a promising new framework for XC functional design, although challenges remain in obtaining training data and generating models consistent with pseudopotentials.

References in corpus (22)

• Adam: A Method for Stochastic Optimization
• Van der Waals Density Functional for General Geometries
• A real-space grid implementation of the Projector Augmented Wave method
• Van der Waals density functional: Self-consistent potential and the nature of the van der Waals bond
• Machine Learning of Accurate Energy-Conserving Molecular Force Fields
• Big Data meets Quantum Chemistry Approximations: The $\Delta$-Machine Learning Approach
• By-passing the Kohn-Sham equations with machine learning
• Finding Density Functionals with Machine Learning
• Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
• Ab initio theory and modeling of water
• Van der Waals forces in density functional theory: perturbational long-range electron interaction corrections
• A Machine Learning Potential for Graphene
• Density Functionals that Recognize Covalent, Metallic, and Weak Bonds
• Deep learning and the Schrödinger equation
• Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters
• Automatic differentiation in quantum chemistry with an application to fully variational Hartree-Fock
• Semiclassical atom theory applied to solid-state physics
• Collapse of the Electron Gas to Two Dimensions in Density Functional Theory
• Dimensional crossover of the exchange-correlation energy at the semilocal level
• Tree based machine learning framework for predicting ground state energies of molecules

Cited by in corpus (20)

• Opportunities and Challenges for Machine Learning in Materials Science
• Machine learning for electronically excited states of molecules
• Perspective on integrating machine learning into computational chemistry and materials science
• A Deep Dive into Machine Learning Density Functional Theory for Materials Science and Chemistry
• Advances of Machine Learning in Materials Science: Ideas and Techniques
• Learning the exchange-correlation functional from nature with fully differentiable density functional theory
• DeePKS: a comprehensive data-driven approach towards chemically accurate density functional theory
• Machine learning and excited-state molecular dynamics
• CIDER: An Expressive, Nonlocal Feature Set for Machine Learning Density Functionals with Exact Constraints
• Machine learning density functionals from the random-phase approximation
• Nonlocal Machine-Learned Exchange Functional for Molecules and Solids
• Grad DFT: a software library for machine learning enhanced density functional theory
• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• Mean-Field Density Matrix Decompositions
• Addressing the Band Gap Problem with a Machine-Learned Exchange Functional
• Machine learning for accuracy in density functional approximations
• Inverting the Kohn-Sham equations with physics-informed machine learning
• Data Driven Reaction Mechanism Estimation via Transient Kinetics and Machine Learning
• ElectroLens: Understanding Atomistic Simulations Through Spatially-resolved Visualization of High-dimensional Features
• Neural network distillation of orbital dependent density functional theory