讲座题目：Machine learning approximation in Density Functional Theory

讲座时间：8月19日（星期三）上午10:00-11:30

讲座地点：西安交通大学教学二区化工学院办公楼204会议室

讲座内容摘要：

Machine learning (ML) is an increasingly popular statistical tool for analyzing either measured or calculated data sets. Here we explore its application to a well-defined physics problem, investigating issues of how the underlying physics is handled by ML, and how self-consistent solutions can be found by limiting the domain in which ML is applied. The particular problem is how to find accurate approximate density functionals for the kinetic energy of non-interacting electrons. Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one dimensional box as a functional of their density. The properties of different kernels and methods of  cross-validation are explored, reproducing the physics faithfully in some cases, but not others. We also address how self-consistency can be achieved with   information on only a limited electronic density domain. Accurate constrained  optimal densities are found via a modified Euler-Lagrange constrained minimization of the machine-learned total energy, despite the poor quality of   its functional derivative. A projected gradient descent algorithm is derived    using local principal component analysis. Additionally, a sparse grid representation of the density can be used without degrading the performance of the methods. The implications for machine-learned density functional approximations are discussed.