Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large advances in accuracy and data efficiency for a range of applications in the physical sciences. An outstanding question for equivariant models is why they achieve such larger-than-expected advances in these applications. To probe this question, we examine the role of higher order (non-scalar) features in Euclidean Neural Networks (\texttt{e3nn}). We focus on the previously studied application of \texttt{e3nn} to the problem of electron density prediction, which allows for a variety of non-scalar outputs, and examine whether the nature of the output (scalar $l=0$, vector $l=1$, or higher order $l>1$) is relevant to the effectiveness of non-scalar hidden features in the network. Further, we examine the behavior of non-scalar features throughout training, finding a natural hierarchy of features by $l$, reminiscent of a multipole expansion. We aim for our work to ultimately inform design principles and choices of domain applications for {\tt e3nn} networks.

In a September 2020 essay in Nature Energy, three scientists posed several "grand challenges" -- one of which was to find suitable materials for thermal energy storage devices that could be used in concert with solar energy systems. Fortuitously, Mingda Li -- the Norman C. Rasmussen Assistant Professor of Nuclear Science and Engineering at MIT, who heads the department's Quantum Matter Group -- was already thinking along similar lines. In fact, Li and nine collaborators (from MIT, Lawrence Berkeley National Laboratory, and Argonne National Laboratory) were developing a new methodology, involving a novel machine-learning approach, that would make it faster and easier to identify materials with favorable properties for thermal energy storage and other uses. The results of their investigation appear this month in a paper for Advanced Science. "This is a revolutionary approach that promises to accelerate the design of new functional materials," comments physicist Jaime Fernandez-Baca, a distinguished staff member at Oak Ridge National Laboratory.