In this talk explore a new data-driven approach to the design of exchange-correlation (XC) functionals is explored. The approach, inspired by convolutional filters in computer vision and surrogate functions from optimization, utilizes convolutions of the electron density in order to form a feature space to represent local electronic environments. These features are orbital free, and provide a systematic route to including information at various length scales. Maxwell-Cartesian spherical harmonic kernels are introduced as a rotationally-invariant class of descriptors for the construction of machine-learned functionals. One possible route to machine-learned functionals is demonstrated using data from the B3LYP functional on a number of small-molecules containing C,H,O,N along with neural network regression models. 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 0.1 Angstrom. This suggests 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.

Design and analysis of machine-learning exchange-correlation functionals based on convolutional descriptors

2019 Spring National Meeting

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