14:30 〜 14:45
▲ [18p-225A-6] Machine learning of kinetic energy density functionals for large-scale ab initio modeling
キーワード：machine learning, orbital free density functional theory, neural network
Large-scale ab initio modeling is required to model properties of materials at realistic time and length scales. The near-cubic scaling of Kohn Sham DFT with system size limits routine modeling to systems on the order of 100 atoms. This scaling is due to reliance on orbitals. Orbital-Free DFT (OF-DFT) avoids orbitals and allows for near-linear scaling; up to 105 atoms can be routinely modeled on a desktop. The Achilles’ heel of OF-DFT is the poor quality of available kinetic energy functionals (KEF) which replace the non-interacting kinetic energy T or kinetic energy density (KED) t(r) based on orbitals with a functional of electron density only. This problem is so bad that as of today, OF-DFT cannot be used in applications beyond light metals. We present the results of applying machine learning using neural networks (NN) to learn the KS KED of bulk light metals (Li, Mg, Al), a bulk semiconductor (Si) and molecules (H2O and C6H6). We train the NN using terms of the 4th order gradient expansion as inputs. We achieve ultra-low fit errors with no NN overfitting (contrary to other works). KS KED can be reproduced very accurately for Li, Mg, and Al; most importantly, a very good fit was also achieved for Si - a much more difficult case. A decent fit was achieved for H2O KED, but not for C6H6. We also highlight the critical role played by the type of pseudopotential as well as by KED data distribution, suggesting directions of further research.