Boltzmann inversion: measuring forces by watching movies

Reconstructing effective interaction potentials from structural data is a central inverse problem in statistical physics, particularly relevant for coarse-grained modelling of polymer and colloidal interactions. In this work, we introduce an enhanced version of the Iterative Boltzmann Inversion method for recovering pairwise interaction potentials from a target radial distribution function. Standard iterative schemes require costly many-body simulations at each step to update structural observables. We overcome this bottleneck by incorporating the Borgis force-based estimator for the radial distribution function, which allows the inversion procedure to proceed directly from a fixed ensemble of particle configurations. This approach preserves the minimal-assumption philosophy of Iterative Boltzmann Inversion while significantly improving computational efficiency. We validate the method across a diverse set of benchmark potentials, including Lennard-Jones, Weeks-Chandler-Andersen, power-law and shoulder-type interactions, demonstrating accurate reconstructions even under undersampled or experimental-like conditions. The framework is particularly suited for systems where running repeated simulations is too expensive or impractical, such as when working with large colloidal systems or active matter. These results highlight the potential of force-based inversion schemes as practical and robust tools for effective interaction reconstruction.