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

[Sajid Ali]

Hi PETSc-developers,

Could the code used for section 5.1 of the recent paper "PETSc TSAdjoint: a
discrete adjoint ODE solver for first-order and second-order sensitivity
analysis" be shared ? Are there more examples that deal with time dependent
parameters in the git repository ?

Another question I have is regarding the equations used to introduce
adjoints in section 7.1 of the manual where for the state of the solution
vector is denoted by y and the parameters by p.

[1] I'm unsure about what the partial derivative of y0 with respect to p
means since I understand y0 to be the initial conditions used to solve the
TS which would not depend on the parameters (since the parameters are
related to the equations TS tries to solve for which should not dependent
on the initialization used). Could someone clarify what this means ?

[2] The manual described that a user has to set the correct initialization
for the adjoint variables when calling TSSetCostGradients. The
initialization for mu vector is whereby given to be dΦi/dp at t=tF. If p is
time dependent, does one evaluate this derivative with respect to p(t) at
t=tF ?

Thank You,
Sajid Ali | PhD Candidate
Applied Physics
Northwestern University
s-sajid-ali.github.io
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