  Global machine learning force fields (MLFFs), that have the capacity to
capture collective many-atom interactions in molecular systems, currently only
scale up to a few dozen atoms due a considerable growth of the model complexity
with system size. For larger molecules, locality assumptions are typically
introduced, with the consequence that non-local interactions are poorly or not
at all described, even if those interactions are contained within the reference
ab initio data. Here, we approach this challenge and develop an exact iterative
parameter-free approach to train global symmetric gradient domain machine
learning (sGDML) force fields for systems with up to several hundred atoms,
without resorting to any localization of atomic interactions or other
potentially uncontrolled approximations. This means that all atomic degrees of
freedom remain fully correlated in the global sGDML FF, allowing the accurate
description of complex molecules and materials that present phenomena with
far-reaching characteristic correlation lengths. We assess the accuracy and
efficiency of our MLFFs on a newly developed MD22 benchmark dataset containing
molecules from 42 to 370 atoms. The robustness of our approach is demonstrated
in nanosecond long path-integral molecular dynamics simulations for the
supramolecular complexes in the MD22 dataset.
