AuthorsS. W. Funke
TitleAutomated adjoints for finite element models
AfilliationScientific Computing
Project(s)OptCutCell: Simulation-based optimisation with dynamic domains
StatusPublished
Publication TypeTalk, keynote
Year of Publication2018
Location of TalkEUCCO 2018, Trier, Germany
Abstract

Adjoints of partial differential equations (PDEs) play an key role in solving optimization
problems constrained by physical laws. The adjoint model efficiently computes gradient and
Hessian 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-dependent
PDE models is notoriously difficult.
In this talk, we solve this problem by automatically deriving adjoint models for finite
element models. Our approach raises the level of abstraction of algorithmic differentiation
from the level of individual floating point operations to that of entire systems of differential
equations. For each differential equation, the algorithm analyses and exploits the high-level
mathematical structure inherent in finite element methods to derive its adjoint. We demons-
trate that this strategy has advantages over traditional algorithmic differentiation: the adjoint
model is robustly obtained with minimal code changes, yields close-to-optimal performance
and 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 showcase
some of the new features, including differentiation with respect to Dirichlet boundary condi-
tions, automated shape derivatives, and the experimental integration with a machine learning
framework. In addition, we show applications where dolfin-adjoint has already been employed.

Citation Key26153

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