i will talk about two recent projects on solving inverse problems for kinetic models, where a change of perspective between lagrangian and eulerian is highly beneficial. in the first project, we are interested in recovering the initial temperature of the nonlinear boltzmann equation given macroscopic quantities observed at a later time. with the problem formulated as constrained optimization, our proposed adjoint dsmc method, together with the well-known (forward) dsmc method, makes it possible to evaluate boltzmann-constrained gradient within seconds, independent of the size of the parameter. in the second project, we are interested in calibrating the parameter in the chaotic dynamic system. transforming the long-time trajectories to an invariant measure significantly improves the inverse problem's ill-posedness. it also turns the original ode model into a pde model (continuity equation or fokker-planck equation), allowing efficient gradient calculation for the resulting pde-constrained optimization problem.