  Neural network interatomic potentials (NNIPs) are an attractive alternative
to ab-initio methods for molecular dynamics (MD) simulations. However, they can
produce unstable simulations which sample unphysical states, limiting their
usefulness for modeling phenomena occurring over longer timescales. To address
these challenges, we present Stability-Aware Boltzmann Estimator (StABlE)
Training, a multi-modal training procedure which combines conventional
supervised training from quantum-mechanical energies and forces with reference
system observables, to produce stable and accurate NNIPs. StABlE Training
iteratively runs MD simulations to seek out unstable regions, and corrects the
instabilities via supervision with a reference observable. The training
procedure is enabled by the Boltzmann Estimator, which allows efficient
computation of gradients required to train neural networks to system
observables, and can detect both global and local instabilities. We demonstrate
our methodology across organic molecules, tetrapeptides, and condensed phase
systems, along with using three modern NNIP architectures. In all three cases,
StABlE-trained models achieve significant improvements in simulation stability
and recovery of structural and dynamic observables. In some cases,
StABlE-trained models outperform conventional models trained on datasets 50
times larger. As a general framework applicable across NNIP architectures and
systems, StABlE Training is a powerful tool for training stable and accurate
NNIPs, particularly in the absence of large reference datasets.
