On adjoint models, their implementation and applications

Time: 15:50 - 16:10  The adjoint equations of partial differential equations are essential in computational science. They enable the study of the sensitivity and stability of solutions, and the optimisation of free... [ view full abstract ]

Time: 15:50 - 16:10  

The adjoint equations of partial differential equations are essential in computational science. They enable the study of the sensitivity and stability of solutions, and the optimisation of free parameters. For practical problems however, the application of adjoints is often hindered by their difficult derivation and implementation, particularly for coupled, nonlinear and time-dependent models. In [1], the authors proposed an approach of automatically implementing adjoint models by exploiting the high-level mathematical structure inherent in finite element methods. In 2015, this idea was awarded the Wilkinson prize, and has since then been used to introduce adjoints to new application areas, ranging from renewable energy to biomedical computing.
In this talk, we give an introduction to adjoint models and the idea of high-level adjoint derivations. We then present a set of applications from biomedical computing and other disciplines where adjoint models have been used.

[1] PE Farrell, DA Ham, SW Funke and ME Rognes (2013). Automated derivation of the adjoint of high-level transient finite element programs, SIAM Journal on Scientific Computing