Keywords

unsteady discrete adjoint, automatic differentiation, algorithmic differentiation, vortex particle method, VPM, fast multipole method, FMM, reverse-mode, pullback, custom rule

Abstract

Automatic differentiation (AD) is a powerful tool for evaluating numerical derivatives. In particular, reverse-mode AD provides numerical gradients in a way that is insensitive to the number of input variables. This makes reverse-mode AD well-suited for solving large optimization problems. However, reverse-mode AD has a particularly large associated memory cost because most intermediate values in operations need to be cached. This is problematic for large problems such as aerodynamics simulations, though, since the memory requirements can quickly become impractical. The solution implemented in this work is to provide analytic pullback expressions for functions for which many of the intermediate values are not needed. This solution is then applied to a vortex-particle method simulation to obtain numerical derivatives significantly faster.

Original Publication Citation

Green, E., and Ning, A., “Derivative Propagation Through Vortex Particle Method Simulation,” AIAA Aviation Forum, Las Vegas, Jul. 2024. doi:10.2514/6.2024-4295