The ability of eukaryotic cells to squeeze through constrictions is limited by the stiffness of their large and rigid nucleus. However, migrating cells are often able to overcome this limitation and pass through constrictions much smaller than their nucleus, a mechanism that is not yet understood. Here, we propose a methodological framework to observe, quantify, and model this nuclear translocation phenomenon through a data-driven approach using microfluidic devices where cells migrate through controlled narrow spaces of sizes comparable to the ones encountered in physiological situations. Stochastic force inference is applied to experimental nuclear trajectories and nuclear shape descriptors, resulting in equations that effectively describe the kinematics of this nuclear translocation phenomenon. By employing a model where the channel geometry is an explicit parameter and by training it over experimental data with different sizes of constrictions, we ensure that the resulting equations are predictive. Altogether, the approach developed here paves the way for a mechanistic and quantitative description of dynamical cell complexity during its motility.