KineticNet: Deep learning a transferable kinetic energy functional for orbital-free density functional theory

Abstract

Orbital-free density functional theory (OF-DFT) holds the promise to compute ground state molecular properties at minimal cost. However, it has been held back by our inability to compute the kinetic energy as a functional of the electron density only. We here set out to learn the kinetic energy functional from ground truth provided by the more expensive Kohn-Sham density functional theory. Such learning is confronted with two key challenges: Giving the model sufficient expressivity and spatial context while limiting the memory footprint to afford computations on a GPU; and creating a sufficiently broad distribution of training data to enable iterative density optimization even when starting from a poor initial guess. In response, we introduce KineticNet, an equivariant deep neural network architecture based on point convolutions adapted to the prediction of quantities on molecular quadrature grids. Important contributions include convolution filters with sufficient spatial resolution in the vicinity of the nuclear cusp, an atom-centric sparse but expressive architecture that relays information across multiple bond lengths; and a new strategy to generate varied training data by finding ground state densities in the face of perturbations by a random external potential. KineticNet achieves, for the first time, chemical accuracy of the learned functionals across input densities and geometries of tiny molecules. For two electron systems, we additionally demonstrate OF-DFT density optimization with chemical accuracy.

arXiv commentThis article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in The Journal of Chemical Physics 159, 144113 (2023) and may be found at https://doi.org/10.1063/5.0158275

References in corpus (13)

• Adam: A Method for Stochastic Optimization
• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Recent developments in the PySCF program package
• Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
• Symmetry-Adapted Machine-Learning for Tensorial Properties of Atomistic Systems
• 3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
• Orbital-free Bond Breaking via Machine Learning
• Machine Learning the Physical Non-Local Exchange-Correlation Functional of Density-Functional Theory
• Kinetic energy densities based on the fourth order gradient expansion: performance in different classes of materials and improvement via machine learning
• Toward Orbital-Free Density Functional Theory with Small Data Sets and Deep Learning
• Order-$N$ orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals
• Robust All-Electron Optimization in Orbital-Free Density Functional Theory Using the Trust Region Image Method
• Direct Scheme Calculation of the Kinetic Energy Functional Derivative Using Machine Learning

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