Definition of Term: Adjoint

An adjoint is an extension to a simulator which produces derivatives of the simulator output with respect to its inputs.

Technically, an adjoint is the transpose of a tangent linear approximation; written either by hand or with the application of automatic differentiation, it produces partial derivatives in addition to the standard output of the simulator. An adjoint is computationally more expensive to run than the standard simulator, but efficiency is achieved in comparison to the finite differences method to generating derivatives. This is because where computing partial derivatives by finite differences requires at least two runs of the simulator for each input parameter, the corresponding derivatives can all be generated by one single run of an appropriate adjoint.