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firedrake@imperial.ac.uk

April 2017

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Re: [firedrake] Parameter estimation and optimal experimental design with Firedrake
by David Ham 02 Apr '17

02 Apr '17

Hi Henrik, OK, for this you need Dolfin-adjoint which, despite its name, also works with Firedrake. Dolfin-adjoint solves the adjoint to a PDE solved with Firedrake, including the time-dependent case, with respect to a user-defined functional which can be a function of both space and time. Dolfin-adjoint also wraps several popular optimisation packages to provide a high level interface to solve the optimisation problem, You install Dolfin-adjoint in Firedrake by running: firedrake-update --adjoint This will install dolfin-adjoint and libadjoint in the Firedrake virtualenv, and future updates will update dolfin-adjoint as well as the rest of Firedrake. Once you've installed, dolfin-adjoint is documented at dolfin-adjoint.org . Most of the documentation there refers to FEniCS, but working with Firedrake is essentially identical. There is an example optimisation problem in the Firedrake Jupyter Notebooks ( http://firedrakeproject.org/notebooks.html) and you can also look at the Firedrake tests in dolfin-adjoint, which will be installed in src/dolfin-adjoint/tests_firedrake Cheers, David On Fri, 31 Mar 2017 at 20:48 Buesing, Henrik <HBuesing(a)eonerc.rwth-aachen.de> wrote: > Dear all, > > > > How would I do parameter estimation (and optimal experimental design) in > Firedrake? > > > > I have a time-dependent forward model consisting of a PDE system and > depending on certain parameters. I also have time-dependent > measurements/data. Now, I would like to minimize some functional, which > measures the distance from the forward model to the recorded data. > > > > How would I do this in Firedrake? Is there an example for this? > > > > In a next step, I would like to do optimal experimental design, where one > maximizes the Fisher information (e.g. minimize the trace of the inverse of > the information matrix) with respect to position. > > > > Any ideas on how to approach this? > > Thank you for your help! > Henrik > > > > > > -- > > Dipl.-Math. Henrik Büsing > > Institute for Applied Geophysics and Geothermal Energy > > E.ON Energy Research Center > > RWTH Aachen University > > > > Mathieustr. | Tel +49 (0)241 80 49907 <+49%20241%208049907> > > 52074 Aachen, Germany | Fax +49 (0)241 80 49889 <+49%20241%208049889> > > > > http://www.eonerc.rwth-aachen.de/GGE > > hbuesing(a)eonerc.rwth-aachen.de > > > -- Dr David Ham Department of Mathematics Imperial College London

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