The accuracy of atomistic simulations critically depends on the precision of force fields, yet traditional, numerical methods often struggle to optimize the potential parameters for reproducing target properties. While recent approaches rely on training these force fields based on first-principle simulations, this alone cannot capture complex material responses such as vibrational, or elastic properties. To this extent, we introduce a framework, employing inner loop simulations and outer loop optimization, that exploits automatic differentiation for both property prediction and force-field optimization by computing gradients of the simulation analytically. We demonstrate the approach by optimizing classical Stillinger-Weber and EDIP potentials for silicon systems to reproduce the elastic constants, vibrational density of states, and phonon dispersion. We also demonstrate how a machine-learned potential can be fine-tuned using automatic differentiation to reproduce any target property such as radial distribution functions. Interestingly, the resulting force field exhibits significantly improved accuracy and generalizability to unseen temperatures than those fine-tuned on energy and force. Finally, we demonstrate the extension of the approach to optimize the force fields towards multiple target properties. Altogether, differentiable simulation, through the analytical computation of gradients of the simulation, offers a powerful tool for both theoretical exploration and practical applications toward understanding physical systems and materials.