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<p class="MsoNormal">Ok, I was not able to get such case to work in my firedrake-ts implementation. Maybe I am missing something in my code. I looked at the TSAdjoint paper
<a href="https://arxiv.org/pdf/1912.07696.pdf">https://arxiv.org/pdf/1912.07696.pdf</a> Equation 2.1 and at the adjoint method for the theta method (Equation 2.15) where the mass matrix is not differentiated w.r.t. the design parameter “p” and decided to ask
the question. Is the actual implementation different from what is in the paper?<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Thanks<o:p></o:p></p>
<p class="MsoNormal">Miguel<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">"Zhang, Hong" <hongzhang@anl.gov><br>
<b>Date: </b>Friday, December 18, 2020 at 3:11 PM<br>
<b>To: </b>"Salazar De Troya, Miguel" <salazardetro1@llnl.gov><br>
<b>Cc: </b>Satish Balay via petsc-users <petsc-users@mcs.anl.gov><br>
<b>Subject: </b>Re: [petsc-users] Support for full jacobianP in TSSetIJacobianP<o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-left:.5in">The current interface is general and should be applicable to this case as soon as users can provide IJacobianP, which is dF(Udot,U,P,t)/dP. Were you able to generate it in firedrake? If so, could you provide an
example that I can test? <o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">Thanks,<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">Hong<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">On Dec 18, 2020, at 10:58 AM, Salazar De Troya, Miguel <<a href="mailto:salazardetro1@llnl.gov">salazardetro1@llnl.gov</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">Yes, that is the case I am considering. The special case I am concerned about is as following: the heat equation in variational form and in firedrake/UFL notation is as follows: p*u_t*v*dx + inner(grad(u), grad(v))*dx
= 0, where u is the temperature, u_t is its time derivative, v is just the test function, dx is the integration domain and p is the design parameter. If “p” were discontinuous, one can’t just factor “p” into the second term due to the divergence theorem. Meaning
that p*u_t*v*dx + inner(grad(u), grad(v))*dx = 0 is different than u_t*v*dx + inner(1.0 / p * grad(u), grad(v))*dx = 0, which is what ideally one would obtain in order to adapt to the current interface in TSAdjoint.<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">Thanks<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">Miguel<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"><b><span style="font-size:12.0pt">From:<span class="apple-converted-space"> </span></span></b><span style="font-size:12.0pt">"Zhang, Hong" <<a href="mailto:hongzhang@anl.gov">hongzhang@anl.gov</a>><br>
<b>Date:<span class="apple-converted-space"> </span></b>Thursday, December 17, 2020 at 7:25 PM<br>
<b>To:<span class="apple-converted-space"> </span></b>"Salazar De Troya, Miguel" <<a href="mailto:salazardetro1@llnl.gov">salazardetro1@llnl.gov</a>><br>
<b>Cc:<span class="apple-converted-space"> </span></b>Satish Balay via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] Support for full jacobianP in TSSetIJacobianP</span><o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">Hi Miguel,<span class="apple-converted-space"> </span><o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">Thank you for the nice work. I do not understand what you propose to do here. What is the obstacle to using current TSSetIJacobianP() for the corner case you mentioned? Are you considering a case in which the mass
matrix is parameterized, e.g. M(p) udot - f(t,u) = g(t,u) ?<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">Thanks,<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">Hong<span class="apple-converted-space"> </span><o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">On Dec 17, 2020, at 3:38 PM, Salazar De Troya, Miguel via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"><span lang="ES">Hello,</span><o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"><span lang="ES"> </span><o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">I am working on hooking up TSAdjoint with pyadjoint through the firedrake-ts interface (<a href="https://github.com/IvanYashchuk/firedrake-ts"><span style="color:#0563C1">https://github.com/IvanYashchuk/firedrake-ts</span></a>).
I have done most of the implementation and now I am just testing for corner cases. One of them is when the design variable is multiplying the first derivative term. It would be the case ofF(Udot,U,P,t) = G(U,P,t) in<span class="apple-converted-space"> </span><a href="https://www.mcs.anl.gov/petsc/petsc-master/docs/manualpages/Sensitivity/TSSetIJacobianP.html"><span style="color:#0563C1">https://www.mcs.anl.gov/petsc/petsc-master/docs/manualpages/Sensitivity/TSSetIJacobianP.html</span></a><span class="apple-converted-space"> </span>.
I imagine that one could think of refactoring the “P” in the left hand side to the right hand side, but this is not trivial when “P” is a discontinuous field over the domain. I think it would be better to include the case of F(Udot,U,P,t) = G(U,P,t) in TSSetIJacobianP
and I am volunteering to do it. Given the current implementation of TSAdjoint, is this something feasible?<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">Thanks<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in">Miguel<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"><span lang="ES" style="font-size:9.0pt;font-family:Consolas">Miguel A. Salazar de Troya</span><o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:9.0pt;font-family:Consolas">Postdoctoral Researcher, Lawrence Livermore National Laboratory</span><o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:9.0pt;font-family:Consolas">B141</span><o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:9.0pt;font-family:Consolas">Rm: 1085-5</span><o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:9.0pt;font-family:Consolas">Ph: 1(925) 422-6411</span><o:p></o:p></p>
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