@misc{15089,
  author = {Simon Funke},
  title = {Automated adjoints for finite element models},
  abstract = {Adjoints of partial differential equations (PDEs) play an key role in solving optimizationproblems constrained by physical laws. The adjoint model efficiently computes gradient andHessian information, and hence allows the use of derivative based optimisation algorithms.While deriving the adjoint model associated with a linear stationary PDE model is straightfor-ward, the derivation and implementation of adjoint models for non-linear or time-dependentPDE models is notoriously difficult.In this talk, we solve this problem by automatically deriving adjoint models for finiteelement models. Our approach raises the level of abstraction of algorithmic differentiationfrom the level of individual floating point operations to that of entire systems of differentialequations. For each differential equation, the algorithm analyses and exploits the high-levelmathematical structure inherent in finite element methods to derive its adjoint. We demons-trate that this strategy has advantages over traditional algorithmic differentiation: the adjointmodel is robustly obtained with minimal code changes, yields close-to-optimal performanceand inherits the parallel performance of the forward model.The library dolfin-adjoint implements this idea as an extension to the FEniCS Project. Recently, a major update to dolfin-adjoint has been a released. This talk will showcasesome of the new features, including differentiation with respect to Dirichlet boundary condi-tions, automated shape derivatives, and the experimental integration with a machine learningframework. In addition, we show applications where dolfin-adjoint has already been employed.},
  year = {2018},
  journal = {EUCCO 2018, Trier, Germany},
}