Center for Design, Manufacturing and Materials, Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, Moscow, 143026, Russia.
Moscow Institute of Physics and Technology (State University), Institutskiy per. 9, Dolgoprudny, Moscow Region, 141700, Russia.
Sci Rep. 2020 May 14;10(1):8000. doi: 10.1038/s41598-020-64619-8.
Density functional theory (DFT) is one of the most widely used tools to solve the many-body Schrodinger equation. The core uncertainty inside DFT theory is the exchange-correlation (XC) functional, the exact form of which is still unknown. Therefore, the essential part of DFT success is based on the progress in the development of XC approximations. Traditionally, they are built upon analytic solutions in low- and high-density limits and result from quantum Monte Carlo numerical calculations. However, there is no consistent and general scheme of XC interpolation and functional representation. Many different developed parametrizations mainly utilize a number of phenomenological rules to construct a specific XC functional. In contrast, the neural network (NN) approach can provide a general way to parametrize an XC functional without any a priori knowledge of its functional form. In this work, we develop NN XC functionals and prove their applicability to 3-dimensional physical systems. We show that both the local density approximation (LDA) and generalized gradient approximation (GGA) are well reproduced by the NN approach. It is demonstrated that the local environment can be easily considered by changing only the number of neurons in the first layer of the NN. The developed NN XC functionals show good results when applied to systems that are not presented in the training/test data. The generalizability of the formulated NN XC framework leads us to believe that it could give superior results in comparison with traditional XC schemes provided training data from high-level theories such as the quantum Monte Carlo and post-Hartree-Fock methods.
密度泛函理论（DFT）是求解多体薛定谔方程的最广泛使用的工具之一。DFT 理论中的核心不确定性是交换关联（XC）泛函，其精确形式仍然未知。因此，DFT 成功的关键部分基于 XC 近似发展的进展。传统上，它们基于在低和高密度极限下的解析解以及量子蒙特卡罗数值计算而构建。然而，XC 插值和函数表示没有一致和通用的方案。许多不同的已开发参数化主要利用一些唯象规则来构建特定的 XC 泛函。相比之下，神经网络（NN）方法可以提供一种通用的方法来参数化 XC 泛函，而无需其函数形式的任何先验知识。在这项工作中，我们开发了 NN XC 泛函，并证明了它们在三维物理系统中的适用性。我们表明，NN 方法可以很好地再现局部密度近似（LDA）和广义梯度近似（GGA）。通过仅改变 NN 第一层中的神经元数量，就可以很容易地考虑局部环境。当应用于不在训练/测试数据中呈现的系统时，所开发的 NN XC 泛函会产生良好的结果。所提出的 NN XC 框架的通用性使我们相信，与传统 XC 方案相比，它可以在提供来自量子蒙特卡罗和后哈特ree-fock 方法等高级理论的训练数据时提供更好的结果。
