Towards Linearly Scaling and Chemically Accurate Global Machine Learning Force Fields for Large Molecules

Abstract: Machine learning force fields (MLFFs) are gradually evolving towards enabling molecular dynamics simulations of molecules and materials with ab initio accuracy but at a small fraction of the computational cost. However, several challenges remain to be addressed to enable predictive MLFF simulations of realistic molecules, including: (1) developing efficient descriptors for non-local interatomic interactions, which are essential to capture long-range molecular fluctuations, and (2) reducing the dimensionality of the descriptors in kernel methods (or a number of parameters in neural networks) to enhance the applicability and interpretability of MLFFs. Here we propose an automatized approach to substantially reduce the number of interatomic descriptor features while preserving the accuracy and increasing the efficiency of MLFFs. To simultaneously address the two stated challenges, we illustrate our approach on the example of the global GDML MLFF; however, our methodology can be equally applied to other models. We found that non-local features (atoms separated by as far as 15$~\r{A}$ in studied systems) are crucial to retain the overall accuracy of the MLFF for peptides, DNA base pairs, fatty acids, and supramolecular complexes. Interestingly, the number of required non-local features in the reduced descriptors becomes comparable to the number of local interatomic features (those below 5$~\r{A}$). These results pave the way to constructing global molecular MLFFs whose cost increases linearly, instead of quadratically, with system size.