petsc-3.14.6 2021-03-30
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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 TSAdjoint routines.


#include "petscts.h"  
PetscErrorCode TSSetCostHessianProducts(TS ts,PetscInt numcost,Vec *lambda2,Vec *mu2,Vec dir)
Logically Collective on TS

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

Notes: 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 lamba2 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








Index of all Sensitivity routines
Table of Contents for all manual pages
Index of all manual pages