Abstract: In this talk, I discuss full waveform inversion as an example of large adjoint problems. This problem is relevant in seismic and medical imaging. I will discuss this in the context of Devito, a domain-specific language for automatically generating high-performance finite-difference solvers. Additionally, I will make deep dives into the implementation of automatic differentiation for this DSL, as well as the use of lossy compression to accelerate these computations.