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

[Stefano Zampini]

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


> 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 <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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