  Machine-learning force fields (MLFF) should be accurate, computationally and
data efficient, and applicable to molecules, materials, and interfaces thereof.
Currently, MLFFs often introduce tradeoffs that restrict their practical
applicability to small subsets of chemical space or require exhaustive datasets
for training. Here, we introduce the Bravais-Inspired Gradient-Domain Machine
Learning (BIGDML) approach and demonstrate its ability to construct reliable
force fields using a training set with just 10-200 geometries for materials
including pristine and defect-containing 2D and 3D semiconductors and metals,
as well as chemisorbed and physisorbed atomic and molecular adsorbates on
surfaces. The BIGDML model employs the full relevant symmetry group for a given
material, does not assume artificial atom types or localization of atomic
interactions and exhibits high data efficiency and state-of-the-art energy
accuracies (errors substantially below 1 meV per atom) for an extended set of
materials. Extensive path-integral molecular dynamics carried out with BIGDML
models demonstrate the counterintuitive localization of benzene--graphene
dynamics induced by nuclear quantum effects and allow to rationalize the
Arrhenius behavior of hydrogen diffusion coefficient in a Pd crystal for a wide
range of temperatures.
