Johannes S. Schmidt

Johannes S. Schmidt, Martin Carrasco, Ernst Röell et al.

Despite an ever-increasing interest in topological deep learning models that target higher-order datasets, there is no consensus on how to evaluate such models. This is exacerbated by the fact that topological objects permit operations, such as structural refinements, that are not appropriate for graph data. In this work, we extend MANTRA, a benchmark dataset containing manifold triangulations, to a larger class of manifolds with more diverse homeomorphism types. We show that, unlike prior claims, both graph neural networks (GNNs) and higher-order message passing (HOMP) methods can saturate the benchmark. However, we find that this is contingent on the right representation and feature assignment, emphasizing their importance in baseline models. We thus provide a novel evaluation protocol based on representational diversity and triangulation refinement. Surprisingly, we find no indication that existing models are capable of generalizing beyond the combinatorial structure of the data. This points towards a research gap in developing models that understand topological structure independent of scale. Our work thus provides the necessary scaffolding to evaluate future models and enable the development of topology-aware inductive biases.

Roman Remme, Tobias Kaczun, Tim Ebert et al.

Hohenberg and Kohn have proven that the electronic energy and the one-particle electron density can, in principle, be obtained by minimizing an energy functional with respect to the density. While decades of theoretical work have produced increasingly faithful approximations to this elusive exact energy functional, their accuracy is still insufficient for many applications, making it reasonable to try and learn it empirically. Using rotationally equivariant atomistic machine learning, we obtain for the first time a density functional that, when applied to the organic molecules in QM9, yields energies with chemical accuracy relative to the Kohn-Sham reference while also converging to meaningful electron densities. Augmenting the training data with densities obtained from perturbed potentials proved key to these advances. This work demonstrates that machine learning can play a crucial role in narrowing the gap between theory and the practical realization of Hohenberg and Kohn's vision, paving the way for more efficient calculations in large molecular systems.