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Simulations with an explicit description of intermolecular forces using electronic structure methods are still not feasible for many systems of interest. As a result, empirical methods such as force fields (FF) have become an established tool for the simulation of large and complex molecular systems. However, the parametrization of FF is time consuming and has traditionally been based largely on experimental data, which is scarce for many functional groups. Recent years have therefore seen increasing efforts to automatize FF parametrization and a move towards FF fitted against quantum-mechanical reference data. Here, we propose an alternative strategy to parametrize intermolecular interactions, which makes use of machine learning and gradient-descent based optimization while retaining a functional form founded in physics. This strategy can be viewed as generalization of existing FF parametrization methods. In the proposed approach, graph neural networks are used in conjunction with automatic differentiation to parametrize physically motivated models to potential-energy surfaces, enabling full automatization and broad applicability in chemical space. As a result, highly accurate FF models are obtained which retain the computational efficiency, interpretability and robustness of classical FF. To showcase the potential of the proposed method, both a fixed-charge model and a polarizable model are parametrized for intermolecular interactions and applied to a wide range of systems including dimer dissociation curves and condensed-phase systems.