ESPResSo Summer School: Dr. Philip Loche

Structural representations for atomistic machine learning

The first step in constructing a regression model or performing a data-driven analysis that aims to predict or elucidate the relationship between the atomic-scale structure of matter and its properties is to transform the Cartesian coordinates of particles into a suitable representation, often referred to as a descriptor or fingerprint. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine learning models for chemistry and materials science.

This lecture will highlight the current understanding of the nature and characteristics of the most commonly used structural and chemical representations of atomistic systems. We will discuss how atom-centered descriptors are designed for atomistic machine learning, focusing on important ingredients such as smoothness, completeness, symmetry, additivity, and invariance with respect to permutations, translations, and rotations, as well as their connection to equivariant representations. We will begin with physics-inspired descriptors such as the smooth overlap of atomic orbitals (SOAP) and Behler–Parrinello symmetry functions, and then move to modern representations used in graph neural networks, as exemplified by state-of-the-art models like MACE, Allegro, PET, and others. The lecture will emphasize the links between properties, structures, their physical chemistry, and their mathematical description, and will provide examples of recent applications to a diverse range of problems in chemistry and materials science.