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<div class="">On Mar 12, 2020, at 8:31 PM, Sajid Ali <<a href="mailto:sajidsyed2021@u.northwestern.edu" class="">sajidsyed2021@u.northwestern.edu</a>> wrote:</div>
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<div class="">Hi Hong, <br class="">
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<div class="">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
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<div class="">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).<br class="">
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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 ?<br class="">
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<div>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</div>
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<div>MatCreateVecs(Jacp,&Mu[0],NULL)</div>
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<div>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.</div>
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<div class="">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.<br class="">
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<div>No, you cannot. Lambda is needed internally by the adjoint solver to calculate the sensitivities wrt parameters.</div>
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Hong</div>
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Thank You, <br class="">
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<div style="font-size:12.8px" class="">Sajid Ali | PhD Candidate<br class="">
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<div style="font-size:12.8px" class="">Applied Physics<br class="">
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<div style="font-size:12.8px" class="">Northwestern University</div>
<div style="font-size:12.8px" class=""><a href="http://s-sajid-ali.github.io/" target="_blank" class="">s-sajid-ali.github.io</a></div>
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