[petsc-users] Questions about TSAdjoint for time dependent parameters

[Zhang, Hong]

On Mar 12, 2020, at 8:31 PM, Sajid Ali <sajidsyed2021 at u.northwestern.edu<mailto:sajidsyed2021 at u.northwestern.edu>> wrote:


Hi Hong,

For the optimal control example, the cost function has an integral term which necessitates the setup of a sub-TS quadrature. The Jacobian with respect to parameter, (henceforth denoted by Jacp) has dimensions that depend upon the number of steps that the TS integrates for.

I'm trying to implement a simpler case where the cost function doesn't have an integral term but the parameters are still time dependent. For this, I modified the standard Van der Pol example (ex20adj.c) to make mu a time dependent parameter (though it has the same value at all points in time and I also made the initial conditions & params independent).

Since the structure of Jacp doesn't depend on time (i.e. it is the same at all points in time, the structure being identical to the time-independent case), is it necessary that I create a Jacp matrix size whose dimensions are [dimensions of time-independent Jacp] * -ts_max_steps ? Keeping Jacp dimensions the same as dimensions of time-independent Jacp causes the program to crash (possibly due to the fact that Jacp and adjoint vector can't be multiplied). Ideally, it would be nice to have a Jacp analog of TSRHSJacobianSetReuse whereby I specify the Jacp routine once and TS knows how to reuse that at all times. Is this possible with the current petsc-master ?

When the parameters are time dependent, they have to be discretized in time. In the optimal control example, the parameter at each discrete point is treated as a new parameter. If you have np time-dependent parameters, you can consider the total number of parameters to be Np = np*the number of discrete points (which is typically the total number of time steps). And you need to create a Jacp matrix of dimension N * Np, where N is the dimension of the ODE system. Mu should have the dimension Np. This is why we can simply create Mu from the matrix with

MatCreateVecs(Jacp,&Mu[0],NULL)

Alternatively, you can set up the solver in the same way that you do for time constant parameters — create a Jacp of N * np and a mu of np. Be aware that after TSAdjointSolve Mu gives only the derivative wrt the parameters at beginning time. You can access the intermediate values of Mu by using a customized TSAdjoint monitor. I think this does what want with a flag like TSRHSJacobianSetReuse.


Another question I have is regarding exclusive calculation of one adjoint. If I'm not interested in adjoint with respect to initial conditions, can I ask TSAdjoing to not calculate that ? Setting the initialization for adjoint vector with respect to initial conditions to be NULL in TSSetCostGradients doesn't work.

No, you cannot. Lambda is needed internally by the adjoint solver to calculate the sensitivities wrt parameters.

Hong


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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