In the last decade, the use of Machine and Deep Learning (MDL) methods in Condensed Matter physics has seen a steep increase in the number of problems tackled and methods employed. A number of distinct MDL approaches have been employed in many different topics; from prediction of materials properties to computation of Density Functional Theory potentials and inter-atomic force fields. In many cases the result is a surrogate model which returns promising predictions but is opaque on the inner mechanisms of its success. On the other hand, the typical practitioner looks for answers that are explainable and provide a clear insight on the mechanisms governing a physical phenomena. In this work, we describe a proposal to use a sophisticated combination of traditional Machine Learning methods to obtain an explainable model that outputs an explicit functional formulation for the material property of interest. We demonstrate the effectiveness of our methodology in deriving a new highly accurate expression for the enthalpy of formation of solid solutions of lanthanides orthophosphates.

翻译：过去十年间，机器学习和深度学习在凝聚态物理中的应用呈指数级增长，所解决的问题类型及采用的方法数量均显著增加。从材料性质预测到密度泛函理论势能函数与原子间力场的计算，多种不同的机器学习和深度学习技术已被广泛应用于各类课题。在许多情况下，其结果是一个代理模型，虽能提供有前景的预测，但对其成功的内在机制缺乏透明度。然而，典型的研究者追求的是可解释的答案，并希望获得对物理现象背后机制的清晰洞察。本研究提出一种方案，通过巧妙组合传统机器学习方法，构建可解释模型，从而为目标材料特性输出显式函数表达式。我们通过推导镧系正磷酸盐固溶体形成焓的高精度新表达式，验证了该方法论的有效性。