Global machine learning force fields, with the capacity to capture collective interactions in molecular systems, now scale up to a few dozen atoms due to considerable growth of model complexity with system size. For larger molecules, locality assumptions are introduced, with the consequence that nonlocal interactions are not described. Here, we develop an exact iterative approach to train global symmetric gradient domain machine learning (sGDML) force fields (FFs) for several hundred atoms, without resorting to any potentially uncontrolled approximations. All atomic degrees of freedom remain 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 sGDML on a newly developed MD22 benchmark dataset containing molecules from 42 to 370 atoms. The robustness of our approach is demonstrated in nanosecond path-integral molecular dynamics simulations for supramolecular complexes in the MD22 dataset.