jats:titleAbstract</jats:title>jats:pMachine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large data set in the first place. Here we present a description of atomic systems that generates machine learning representations with a direct path to physical interpretation. As an example, we demonstrate its usefulness as a universal descriptor of grain boundary systems. Grain boundaries in crystalline materials are a quintessential example of a complex, high-dimensional system with broad impact on many physical properties including strength, ductility, corrosion resistance, crack resistance, and conductivity. In addition to modeling such properties, the method also provides insight into the physical “building blocks” that influence them. This opens the way to discover the underlying physics behind behaviors by understanding which building blocks map to particular properties. Once the structures are understood, they can then be optimized for desirable behaviors.</jats:p>