Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory

We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt$_{2}$, Au$_{2}$, TlF, and Bi$_{2}$Se$_{3}$ indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.Comment: 31 pages, 5 figure

Sampled in Pairs and Driven by Text: A New Graph Embedding Framework

In graphs with rich texts, incorporating textual information with structural information would benefit constructing expressive graph embeddings. Among various graph embedding models, random walk (RW)-based is one of the most popular and successful groups. However, it is challenged by two issues when applied on graphs with rich texts: (i) sampling efficiency: deriving from the training objective of RW-based models (e.g., DeepWalk and node2vec), we show that RW-based models are likely to generate large amounts of redundant training samples due to three main drawbacks. (ii) text utilization: these models have difficulty in dealing with zero-shot scenarios where graph embedding models have to infer graph structures directly from texts. To solve these problems, we propose a novel framework, namely Text-driven Graph Embedding with Pairs Sampling (TGE-PS). TGE-PS uses Pairs Sampling (PS) to improve the sampling strategy of RW, being able to reduce ~99% training samples while preserving competitive performance. TGE-PS uses Text-driven Graph Embedding (TGE), an inductive graph embedding approach, to generate node embeddings from texts. Since each node contains rich texts, TGE is able to generate high-quality embeddings and provide reasonable predictions on existence of links to unseen nodes. We evaluate TGE-PS on several real-world datasets, and experiment results demonstrate that TGE-PS produces state-of-the-art results on both traditional and zero-shot link prediction tasks.Comment: Accepted by WWW 2019 (The World Wide Web Conference. ACM, 2019

Machine-Learned Invertible Coarse Graining for Multiscale Molecular Modeling

Multiscale molecular modeling is widely applied in scientific research of molecular properties over large time and length scales. Two specific challenges are commonly present in multiscale modeling, provided that information between the coarse and fine representations of molecules needs to be properly exchanged: One is to construct coarse grained (CG) models by passing information from the fine to coarse levels; the other is to restore finer molecular details given CG configurations. Although these two problems are commonly addressed independently, in this work, we present a theory connecting them, and develop a methodology called Cycle Coarse Graining (CCG) to solve both problems in a unified manner. In CCG, reconstruction can be achieved via a tractable optimization process, leading to a general method to retrieve fine details from CG simulations, which in turn, delivers a new solution to the CG problem, yielding an efficient way to calculate free energies in a rare-event-free manner. CCG thus provides a systematic way for multiscale molecular modeling, where the finer details of CG simulations can be efficiently retrieved, and the CG models can be improved consistently.Comment: 10 pages, 5 figures, plus S

Influence of oxygen pressure and aging on LaAlO3 films grown by pulsed laser deposition on SrTiO3 substrates

The crystal structures of LaAlO3 films grown by pulsed laser deposition on SrTiO3 substrates at oxygen pressure of 10-3 mbar or 10-5 mbar, where kinetics of ablated species hardly depend on oxygen background pressure, are compared. Our results show that the interface between LaAlO3 and SrTiO3 is sharper when the oxygen pressure is lower. Over time, the formation of various crystalline phases is observed while the crystalline thickness of the LaAlO3 layer remains unchanged. X-ray scattering as well as atomic force microscopy measurements indicate three-dimensional growth of such phases, which appear to be fed from an amorphous capping layer present in as-grown samples