[petsc-users] Converting complex PDE to real for KNL performance ?

[Matthew Knepley]

On Tue, Apr 14, 2020 at 6:26 PM Stefano Zampini <stefano.zampini at gmail.com>
wrote:

> Not true in general when you minimize an objective function as a
> functional of the parameter only
> For same methods (Newton for example, gradient descent, etc) the state
> variables do no enter the minimization, so it should be fine to have
> complex-valued state variables
>

Yes, this was my thinking. Of course, there are problems which do not work,
but I am guessing would could enable
the complex build at least for experts.

  Thanks,

    Matt


> On Apr 15, 2020, at 1:04 AM, Zhang, Hong via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
>
> Sorry for the time travel. As far as I know, optimization over
> complex-valued parameters is not a well-defined problem. I am not sure how
> you can develop an optimization algorithm for it. Perhaps our optimization
> experts have better suggestions in this direction.
>
> The real-valued formulation seems to be more promising to me. The
> preconditioning is hard, but still doable with fieldsplit as Mark mentioned.
>
> Hong (Mr.)
>
> On Apr 14, 2020, at 1:42 PM, Sajid Ali <sajidsyed2021 at u.northwestern.edu>
> wrote:
>
> Hi Hong,
>
> Apologies for creating unnecessary confusion by continuing the old thread
> instead of creating a new one.
>
> While I looked into converting the complex PDE formulation to a real
> valued formulation in the past hoping for better performance, my concern
> now is with TAO being incompatible with complex scalars. I would've
> preferred to keep the complex PDE formulation as is (given that I spent
> some time tuning it and it works well now) for cost function and gradient
> evaluation while using TAO for the outer optimization loop.
>
> Using TAO has the obvious benefit of defining a multi objective cost
> function, parametrized as a fit to a series of measurements and a set of
> regularizers while not having to explicitly worry about differentiating the
> regularizer or have to think about implementing a good optimization scheme.
> But if it converting the complex formulation to a real formulation would
> mean a loss of well conditioned forward solve (and increase in solving time
> itself), I was wondering if it would be better to keep the complex PDE
> formulation and write an optimization loop in PETSc while defining the
> regularizer via a cost integrand.
>
> Thank You,
> Sajid Ali | PhD Candidate
> Applied Physics
> Northwestern University
> s-sajid-ali.github.io
>
>
>
>

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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