  Although machine-learning potentials have recently had substantial impact on
molecular simulations, the construction of a robust training set can still
become a limiting factor, especially due to the requirement of a reference ab
initio simulation that covers all the relevant geometries of the system.
Recognizing that this can be prohibitive for certain systems, we develop the
method of transition tube sampling that mitigates the computational cost of
training set and model generation. In this approach, we generate classical or
quantum thermal geometries around a transition path describing a conformational
change or a chemical reaction using only a sparse set of local normal mode
expansions along this path and select from these geometries by an active
learning protocol. This yields a training set with geometries that characterize
the whole transition without the need for a costly reference trajectory. The
performance of the method is evaluated on different molecular systems with the
complexity of the potential energy landscape increasing from a single minimum
to a double proton-transfer reaction with high barriers. Our results show that
the method leads to training sets that give rise to models applicable in
classical and path integral simulations alike that are on par with those based
directly on ab initio calculations while providing the computational speed-up
we have come to expect from machine-learning potentials.
