Construct exchange-correlation functional via machine learning

Density functional theory has been widely used in quantum mechanical simulations, but the search for a universal exchange-correlation (XC) functional has been elusive. Over the last two decades, machine-learning techniques have been introduced to approximate the XC functional or potential, and recent advances in deep learning have renewed interest in this approach. In this article, we review early efforts to use machine learning to approximate the XC functional, with a focus on the challenge of transferring knowledge from small molecules to larger systems. Recently, the transferability problem has been addressed through the use of quasi-local density-based descriptors, which are rooted in the holographic electron density theorem. We also discuss recent developments using deep-learning techniques that target high-level ab initio molecular energy and electron density for training. These efforts can be unified under a general framework, which will also be discussed from this perspective. Additionally, we explore the use of auxiliary machine-learning models for van der Waals interactions.