Completing density functional theory by machine learning hidden messages from molecules
Authors: Nagai et al Code: https://github.com/ml-electron-project/NNfunctional Library: Pytorch Model: MLP URL: https://www.nature.com/articles/s41524-020-0310-0 Year: 2020/2019
The pioneering studies on ML application of the density functionals have been conducted by Burke and coworkers13,14,15, where the universal Hohenberg–Kohn functional FHK[n] as a sum of the kinetic energy T[n] and the interaction energy functionals Vee[n] was constructed for orbital-free DFT, whose framework avoids the heavy calculation to solve the KS equation. Our approach contrasts to theirs, as we target Vxc and adopt the KS framework. In our previous study 16 [Neural-network-Kohn-Sham-exchange-correlation-potetial], we performed the ML mapping n → Vxc for a two-body model system in one dimension trained using the accurate reference data {n, Vxc} generated by the exact diagonalization and subsequent inversion of the KS equation with varying Vion. Therein, the neural network (NN) form was adopted because of its ability to represent any well-behaved functions with arbitrary accuracy17,18. We have found that, when applied to Vion not referenced in the training, the explicit treatment of the kinetic energy suppresses the effect from spurious oscillation in the predicted Vxc, and it reduces the error of finally obtained n(r). This result suggests that the machine-learning approach to Vxc with the KS equation is a promising route. The challenge is then to make the ML of Vxc feasible for real materials.