Tensor-Field Molecular Dynamics: A Deep Learning model for highly accurate, symmetry-preserving force-fields from small data sets

Simulating the dynamic behavior of molecules and extended materials over large time-scales and with high fidelity has been a long-standing goal in computational physics. Recently, Deep Neural Networks have shown great promise in learning energies and atomic forces from atomistic data, thereby providing access to efficient and accurate interatomic force-fields. However, most existing methods still require the construction of very large reference training sets, consisting of tens of thousands of structures, often computed with expensive first-principles approaches. This provides a challenging bottleneck in the construction of interatomic force-fields, limiting Deep Learning-based approaches to systems for which such large training sets are feasible to generate. We present a framework to learn highly accurate Machine-Learning Force-Fields from small training sets. We show that our proposed method is able to obtain high-accuracy force predictions on a variety of different atomic systems, including organic molecules, bulk solids as well as complex interfaces and discuss the resulting Molecular Dynamics simulations.