Algorithmic Differentiation of programs gives sensitivities or gradients,
useful for instance for :
optimum shape design under constraints, multidisciplinary optimization,
and more generally any algorithm based on local linearization,
inverse problems, such as parameter estimation and in particular
4Dvar data assimilation in climate sciences (meteorology, oceanography),
first-order linearization of complex systems, or higher-order simulations, yielding
reduced models for simulation of complex systems around a given state,
adaption of parameters for classification tools such as Machine Learning systems,
in which Adjoint Differentiation is also known as backpropagation.
mesh adaptation and mesh optimization with gradients or adjoints,
equation solving with the Newton method,
sensitivity analysis, propagation of truncation errors.