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 https://arxiv.org/pdf/1912.07696.pdf 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?
Thanks Miguel From: "Zhang, Hong" <[email protected]> Date: Friday, December 18, 2020 at 3:11 PM To: "Salazar De Troya, Miguel" <[email protected]> Cc: Satish Balay via petsc-users <[email protected]> Subject: Re: [petsc-users] Support for full jacobianP in TSSetIJacobianP 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? Thanks, Hong On Dec 18, 2020, at 10:58 AM, Salazar De Troya, Miguel <[email protected]<mailto:[email protected]>> wrote: 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. Thanks Miguel From: "Zhang, Hong" <[email protected]<mailto:[email protected]>> Date: Thursday, December 17, 2020 at 7:25 PM To: "Salazar De Troya, Miguel" <[email protected]<mailto:[email protected]>> Cc: Satish Balay via petsc-users <[email protected]<mailto:[email protected]>> Subject: Re: [petsc-users] Support for full jacobianP in TSSetIJacobianP Hi Miguel, 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) ? Thanks, Hong On Dec 17, 2020, at 3:38 PM, Salazar De Troya, Miguel via petsc-users <[email protected]<mailto:[email protected]>> wrote: Hello, I am working on hooking up TSAdjoint with pyadjoint through the firedrake-ts interface (https://github.com/IvanYashchuk/firedrake-ts). 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 https://www.mcs.anl.gov/petsc/petsc-master/docs/manualpages/Sensitivity/TSSetIJacobianP.html . 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? Thanks Miguel Miguel A. Salazar de Troya Postdoctoral Researcher, Lawrence Livermore National Laboratory B141 Rm: 1085-5 Ph: 1(925) 422-6411
