This paper presents a semi-empirical method for simulating contact with elastically deformable objects whose force response is learned using entirely data-driven models. A point-based surface representation and an inhomogeneous, nonlinear force response model are learned from a robotic arm acquiring force-displacement curves from a small number of poking interactions. The simulator then estimates displacement and force response when the deformable object is in contact with an arbitrary rigid object. It does so by estimating displacements by solving a Hertzian contact model, and sums the expected forces at individual surface points through querying the learned point stiffness models as a function of their expected displacements. Experiments on a variety of challenging objects show that our approach learns force response with sufficient accuracy to generate plausible contact response for novel rigid objects.