  The quantum theory of atoms in molecules (QTAIM) 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 semi-empirical 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 towards 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.
