Exact constraints and appropriate norms in machine-learned exchange-correlation functionals

Abstract

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to deorbitalize the strongly constrained and appropriately normed (SCAN) functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding use of the orbital dependent kinetic energy density. The performance and transferability of the machine learned functional are demonstrated for molecular and periodic systems.

Artificial intelligence in recommender systems

“…The approaches vary widely, with most being numerical as well as symbolic approach . Some made predictions starting from scratch, some start from the previously established functionals [Zheng et al 2004], or from both , and other approaches incorporate exact physical constraints into the functional form [Hollingsworth et al 2018;Pokharel et al 2022;Nagai et al 2022;Dick and Fernandez-Serra 2021;Gedeon et al 2021]. More details can be found in the recent perspectives and review articles [Burke 2012;Manzhos 2020;Kalita et al 2021;Perdew 2021;Fiedler et al 2022;Kulik et al 2022;Nagai and Akashi 2023].…”

“…Similarly, Sparrow et al [2022] designs a novel set of bell-shaped spline functions as the basis to embed the linear and nonlinear constraints as well as incorporate the implicit smoothness constraint as a regularization term in the learning objective. One group examined the effects of imposing a spin-scaling constraint and the general Lieb-Oxford bound when attempting to reproduce the SCAN functional in a deep neural network, showing improvements from the constraints but limited generalizability when attempting to move from data without chemical bonding to chemically bound systems [Pokharel et al 2022]. Furthermore, to satisfy physical asymptotic constraints, Nagai et al [2022] breaks down the XC energy functional into different terms (e.g., spin-up exchange, spin-down exchange energy, correlation energy), analytically imposes asymptotic constraints on different neural modules and aggregates all the NNs' output.…”

A Semilocal Machine-Learning Correction for Density Functional Approximations

“…The resulting DM21 functional has demonstrated promising performance for the treatment of charge delocalization and strong correlation. Pokharel et al have designed a deep neural network to de-orbitalize the strongly constrained and appropriately normed (SCAN) functional [5], and the resulting ML functional replicates the performance of SCAN by utilizing the information of electron density and density derivative while avoiding the use of the orbital-dependent kinetic energy density [54]. Recently, Nagai et al have constructed an MLcorrected SCAN functional [37].…”

A Semilocal Machine-Learning Correction to Density Functional Approximations

“…The resulting DM21 functional has demonstrated promising performance for the treatment of charge delocalization and strong correlation. Pokharel et al have designed a deep neural network to de-orbitalize the strongly constrained and appropriately normed (SCAN) functional [5], and the resulting ML functional replicates the performance of SCAN by utilizing the information of electron density and density derivative while avoiding the use of the orbital-dependent kinetic energy density [55]. Recently, Nagai et al have constructed an MLcorrected SCAN functional [37].…”