Training and accuracy We find that each of the models rapidly learns the energy and force of these complicated molecular systems, with the learning curves reaching a plateau in most cases before or near 1 000 epochs, as seen on Figure . Using the smaller initial data set we find the best accuracy is Furthermore, we see that sampling the data set with the flat histogram method does not appear to provide more accuracy when tested against a large random sample. However, as observed in the training curves (Figure ), it does appear to learn marginally faster for forces, in our specific case. As a result of the initial training on the smaller data set, we trained a model with l = 2, r = 6 Å without parity (denoted here as "nequip deployed") on a large data set created by flat histogram sampling. This model achieves near DFT accuracy on energy and forces, as summarized in Table . We also trained a model with Allegro, for the purpose of comparison, and in order to be able to perform molecular simulations on much larger systems. As expected, we found out that the strictly local Allegro model has lower accuracy, with a mean average error (MAE) of 0.70 meV on energy per atom (compared to 0.60 for NequIP), and 30.1 meV/ Å on forces (compared to 15.0 for nequip). On the other hand, we will show later than it has great scalability, and it uses only a fraction of the memory that NequIP requires. During our study, we tested several different loss functions to simultaneously minimize the errors on the energy (E), forces ({F i }) and stress (σ) of the system. We found that training MLPs on energy and forces only is sufficient to reproduce the mechanical properties with reasonable accuracy (see Supporting Information) as expected from the errors in stress computed, and that including stress in the optimization of the MLP typically does not improve the quality of the model (and sometimes degrades it with respect to errors on energy and force). While this is counter-intuitive, it may come from the fact that instantaneous stress tensors computed during the ab initio dynamics suffer from a higher relative noise than the energy and forces.