A review of adjoint methods for sensitivity analysis, uncertainty quantification and optimization in numerical codes

The goal of this paper is to briefly recall the importance of the adjoint method in many problems of sensitivity analysis, uncertainty quantification and optimization when the model is a differential equation. We illustrate this notion with some recent examples. As is well known, from a computational point of view the adjoint method is intrusive, meaning that it requires some changes in the numerical codes. Therefore we advocate that any new software development must take into account this issue, right from its inception.