Automated parallel adjoints for model differentiation, optimisation and stability analysis
Abstract
The derivatives of PDE models are key ingredients in many
important algorithms of computational science. They find applications in
diverse areas such as sensitivity analysis, PDE-constrained
optimisation, continuation and bifurcation analysis, error estimation,
and generalised stability theory.
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These derivatives, computed using the so-called tangent linear and
adjoint models, have made an enormous impact in certain scientific fields
(such as aeronautics, meteorology, and oceanography). However, their use
in other areas has been hampered by the great practical
difficulty of the derivation and implementation of tangent linear and
adjoint models. In his recent book, Naumann (2011) describes the problem
of the robust automated derivation of parallel tangent linear and
adjoint models as "one of the great open problems in the field of
high-performance scientific computing''.
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In this talk, we present an elegant solution to this problem for the
common case where the original discrete forward model may be written in
variational form, and discuss some of its applications.