Sets the initial value of the Hessian-vector products of the cost function w.r.t. initial values and w.r.t. the problem parameters for use by the TS adjoint routines.


#include <petscts.h>  
PetscErrorCode TSSetCostHessianProducts(TS ts, PetscInt numcost, Vec *lambda2, Vec *mu2, Vec dir)

Logically Collective

Input Parameters#

  • ts - the TS context obtained from TSCreate()

  • numcost - number of cost functions

  • lambda2 - Hessian-vector product with respect to the initial condition variables, the dimension and parallel layout of these vectors is the same as the ODE solution vector

  • mu2 - Hessian-vector product with respect to the parameters, the number of entries in these vectors is the same as the number of parameters

  • dir - the direction vector that are multiplied with the Hessian of the cost functions


Hessian of the cost function is completely different from Hessian of the ODE/DAE system

For second-order adjoint, one needs to call this function and then TSAdjointSetForward() before TSSolve().

After TSAdjointSolve() is called, the lambda2 and the mu2 will contain the computed second-order adjoint sensitivities, and can be used to produce Hessian-vector product (not the full Hessian matrix). Users must provide a direction vector; it is usually generated by an optimization solver.

Passing NULL for lambda2 disables the second-order calculation.

See Also#

TS: Scalable ODE and DAE Solvers, TS, TSAdjointSolve(), TSAdjointSetForward()







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