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

[Zhang, Hong]

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<mailto: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<http://s-sajid-ali.github.io/>

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