Quantum-chemical insights from interpretable atomistic neural networks

With the rise of deep neural networks for quantum chemistry applications, there is a pressing need for architectures that, beyond delivering accurate predictions of chemical properties, are readily interpretable by researchers. Here, we describe interpretation techniques for atomistic neural networks on the example of Behler-Parrinello networks as well as the end-to-end model SchNet. Both models obtain predictions of chemical properties by aggregating atom-wise contributions. These latent variables can serve as local explanations of a prediction and are obtained during training without additional cost. Due to their correspondence to well-known chemical concepts such as atomic energies and partial charges, these atom-wise explanations enable insights not only about the model but more importantly about the underlying quantum-chemical regularities. We generalize from atomistic explanations to 3d space, thus obtaining spatially resolved visualizations which further improve interpretability. Finally, we analyze learned embeddings of chemical elements that exhibit a partial ordering that resembles the order of the periodic table. As the examined neural networks show excellent agreement with chemical knowledge, the presented techniques open up new venues for data-driven research in chemistry, physics and materials science.