Efficient nonparametricn-body force fields from machine learning

The authors present a scheme to construct classical n-body force fields using Gaussian Process (GP) Regression, appropriately mapped over explicit n-body functions (M-FFs). The procedure is possible, and will yield accurate forces, whenever prior knowledge allows to restrict the interactions to a finite order n, so that the ``universal approximator'' resolving power of standard GPs or Neural Networks is not needed. Under these conditions, the proposed construction preserves flexibility of training, systematically improvable accuracy, and a clear framework for validation of the underlying machine learning technique. Moreover, the M-FFs are as fast as classical parametrized potentials, since they avoid lengthy summations over database entries or weight parameters.