  The need to use a short time step is a key limit on the speed of molecular
dynamics (MD) simulations. Simulations governed by classical potentials are
often accelerated by using a multiple-time-step (MTS) integrator that evaluates
certain potential energy terms that vary more slowly than others less
frequently. This approach is enabled by the simple but limiting analytic forms
of classical potentials. Machine learning interatomic potentials (MLIPs), in
particular recent equivariant neural networks, are much more broadly applicable
than classical potentials and can faithfully reproduce the expensive but
accurate reference electronic structure calculations used to train them. They
still, however, require the use of a single short time step, as they lack the
inherent term-by-term scale separation of classical potentials. This work
introduces a method to learn a scale separation in complex interatomic
interactions by co-training two MLIPs. Initially, a small and efficient model
is trained to reproduce short-time-scale interactions. Subsequently, a large
and expressive model is trained jointly to capture the remaining interactions
not captured by the small model. When running MD, the MTS integrator then
evaluates the smaller model for every time step and the larger model less
frequently, accelerating simulation. Compared to a conventionally trained MLIP,
our approach can achieve a significant speedup (~3x in our experiments) without
a loss of accuracy on the potential energy or simulation-derived quantities.
