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<p class="MsoNormal">Does this mean that the adjoint method doesn’t take into account the step adapter? Meaning that the adapter is not differentiated with respect to its dependencies (one of them being the solution at each time step). I can imagine that a
discrete adjoint method with a step controller should be differentiating the step controller as well.<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>Wednesday, October 28, 2020 at 8:36 PM<br>
<b>To: </b>"Salazar De Troya, Miguel" <salazardetro1@llnl.gov><br>
<b>Cc: </b>"Guyer, Jonathan E. Dr. (Fed) via petsc-users" <petsc-users@mcs.anl.gov><br>
<b>Subject: </b>Re: [petsc-users] TSAdjoint and adaptive time stepping<o:p></o:p></span></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">I think it depends on the functional for which the sensitivities are calculated. For most cases, the objective functional should not be sensitive to the step sizes when a converged solution is achieved. What the
adapter does is just to choose a step size so that the solution is accurate within certain tolerances. Of course, if the adapter is not doing a good job (e.g. choosing a step size that leads to instability), not only the sensitivities are influenced but also
the solution is inaccurate.<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">Hong (Mr.)<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">On Oct 28, 2020, at 4:54 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">Hello,<span style="font-size:12.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-left:.5in"> <span style="font-size:12.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-left:.5in">I saw in the TSAdjoint paper that adjoints for adaptive time stepping schemes are supported. Given that these schemes usually involve nondifferentiable functions to pick the time step, are the sensitivities also
nondifferentiable at certain points? Does one need to be careful when using adjoints with adaptive time steps?<span style="font-size:12.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-left:.5in"> <span style="font-size:12.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-left:.5in"><span lang="ES">Thanks</span><span style="font-size:12.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-left:.5in"><span lang="ES">Miguel</span><span style="font-size:12.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-left:.5in"><span lang="ES"> </span><span style="font-size:12.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-left:.5in"><span lang="ES"> </span><span style="font-size:12.0pt"><o:p></o:p></span></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><span style="font-size:12.0pt"><o:p></o:p></span></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><span style="font-size:12.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:9.0pt;font-family:Consolas">B141</span><span style="font-size:12.0pt"><o:p></o:p></span></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><span style="font-size:12.0pt"><o:p></o:p></span></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><span style="font-size:12.0pt"><o:p></o:p></span></p>
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