Computing formation enthalpies through an explainable machine learning method: the case of lanthanide orthophosphates solid solutions

Frontiers in Applied Mathematics and Statistics, vol. 10

Abstract

In the last decade, the use of AI in Condensed Matter physics has seen a steep increase in the number of problems tackled and methods employed. A number of distinct Machine Learning approaches have been employed in many different topics; from prediction of material 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 into the mechanisms governing a physical phenomena. In this study, 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 lanthanide orthophosphates.

Authors 4

1. Edoardo Di Napoli corresponding

   Forschungszentrum Jülich · Jülich Aachen Research Alliance · Jülich Supercomputing Centre

   Affiliation as printed

   Jülich Aachen Research Alliance Center for Simulation and Data Science, Forschungszentrum Jülich, Jülich, Germany

   Simulation and Data Lab Quantum Materials, Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany

   Jülich Aachen Research Alliance Center for Simulation and Data Science, Forschungszentrum Jülich, Germany

   Simulation and Data Lab Quantum Materials, Jülich Supercomputing Centre, Forschungszentrum Jülich, Germany

2. Xinzhe Wu

   Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Simulation and Data Lab Quantum Materials, Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany

   Simulation and Data Lab Quantum Materials, Jülich Supercomputing Centre, Forschungszentrum Jülich, Germany

3. Thomas Bornhake Aachen Physics Department

   RWTH Aachen University

   Affiliation as printed

   Physics Department, RWTH Aachen University, Aachen, Germany

   Physics Department, RWTH Aachen University, Germany

4. Piotr M. Kowalski

   Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   Institute of Energy and Climate Research (IEK-13), Forschungszentrum Jülich, Jülich, Germany

   Jülich Aachen Research Alliance Center for Simulation and Data Science, Forschungszentrum Jülich, Jülich, Germany

   Jülich Aachen Research Alliance Energy, Forschungszentrum Jülich, Jülich, Germany

   Institute of Energy and Climate Research (IEK-13), Forschungszentrum Jülich, Germany

   Jülich Aachen Research Alliance Center for Simulation and Data Science, Forschungszentrum Jülich, Germany

   Jülich Aachen Research Alliance Energy, Forschungszentrum Jülich, Germany