Abstract

We derive adjoint equations for Direct Simulation Monte Carlo (DSMC) methods applied to the spatially inhomogeneous Boltzmann equation. The formulation incorporates spatial transport and a range of boundary conditions, including periodic boundaries, specular and thermal reflection, and prescribed inflow. The resulting adjoint system enables efficient gradient evaluation for quantities of interest defined through particle-based simulations. Numerical experiments validate the accuracy of the adjoint formulation and demonstrate its use in sensitivity analysis and gradient-based optimization. This work provides a foundation for integrating kinetic-scale particle methods into multi-fidelity optimization and control frameworks, with potential applications to rarefied plasma flows and edge physics in fusion devices.