Emergence of accurate atomic energies from machine-learned noble-gas potentials

The quantum theory of atoms in molecules gives access to well-defined local atomic energies. Due to their locality, these energies are potentially interesting in fitting atomistic machine learning models as they inform about physically relevant properties. However, computationally, quantum-mechanically accurate local energies are notoriously difficult to obtain for large systems. Here, we show that by employing semiempirical correlations between different components of the total energy, we can obtain well-defined local energies at a moderate cost. We employ this methodology to investigate energetics in noble liquids or argon, krypton, and their mixture. Instead of using these local energies to fit atomistic models, we show how well these local energies are reproduced by machine-learned models trained on the total energies. The results of our investigation suggest that smaller neural networks, trained only on the total energy of an atomistic system, are more likely to reproduce the underlying local energy partitioning faithfully than larger networks. Furthermore, we demonstrate that networks more capable of this energy decomposition are, in turn, capable of transferring to previously unseen systems. Our results are a step toward understanding how much physics can be learned by neural networks and where this can be applied, particularly how a better understanding of physics aids in the transferability of these neural networks.