The interaction between two anisotropic bodies depends on their relative translation and orientation (i.e., six coordinates), but the functional form of these interactions is not easily described. Machine-learning strategies have recently been employed successfully as data-driven approximations of the pair potential or its corresponding forces and torques, but they have also typically required large training data sets that may be challenging to collect in some contexts. Here, we introduce a data-efficient framework based on multivariate polynomials that systematically samples the configuration space for two anisotropic bodies. We exploit physical knowledge to introduce a variable transformation, enforce symmetry, and select polynomials that produce a better approximation. We then sample and fit the pairwise force and torque at prescribed sample points in the approximation domain using multivariate polynomials. We demonstrate our framework on two-dimensional and three-dimensional nanoparticles and assess its accuracy. We anticipate that our approach may be particularly helpful for constructing coarse-grained models for anisotropic bodies when training data is scarce.
