We outline the general framework of machine learning (ML) methods for multi-scale dynamical modeling of condensed matter systems, and in particular of strongly correlated electron models. Complex spatial temporal behaviors in these systems often arise from the interplay between quasi-particles and the emergent dynamical classical degrees of freedom, such as local lattice distortions, spins, and order-parameters. Central to the proposed framework is the ML energy model that, by successfully emulating the time-consuming electronic structure calculation, can accurately predict a local energy based on the classical field in the intermediate neighborhood. In order to properly include the symmetry of the electron Hamiltonian, a crucial component of the ML energy model is the descriptor that transforms the neighborhood configuration into invariant feature variables, which are input to the learning model. A general theory of the descriptor for the classical fields is formulated, and two types of models are distinguished depending on the presence or absence of an internal symmetry for the classical field. Several specific approaches to the descriptor of the classical fields are presented. Our focus is on the group-theoretical method that offers a systematic and rigorous approach to compute invariants based on the bispectrum coefficients. We propose an efficient implementation of the bispectrum method based on the concept of reference irreducible representations. Finally, the implementations of the various descriptors are demonstrated on well-known electronic lattice models.
翻译:我们概述了机器学习(ML)方法的总体框架,用于对精密物质系统进行多尺度动态建模,特别是具有强烈关联的电子模型。这些系统中复杂的空间时间行为往往产生于准粒子和新兴的动态传统自由度之间的相互作用,例如地方变形、旋转和秩序参数。拟议框架的核心是ML能源模型,该模型通过成功模拟耗时电子结构的计算,可以准确预测基于中间周边古典域的当地能源。为了适当包括电子汉密尔顿仪的对称,ML能源模型的一个关键组成部分是将邻里配置转换成变化性特性变量的描述符,这些变量是学习模型的投入。制定了经典域的描述符的一般理论,根据古典域内部对称的存在或缺失而区分出两种模型。对古典域的典型域的描述仪提出了几种具体的方法。我们的重点是以集团-理论参考模型为主,以系统化的稳妥性模型为基础,以精确的稳妥度方法提出稳妥的稳妥性模型。我们的重点是以稳妥的稳妥性模型为基础,以稳妥性方法提出稳妥的稳妥性方法执行。