Abstract
Estimation of parameters in P.D.E.'s is usually solved as a nonlinear optimization problem, whose cost function is the least square error between computed and recorded data. This requires che calculation of the gradient of the cost function by hand, which includes the determination of the adjoint equation to be solved and of the correlation formulas for the computation of the gradient; this step is often very demanding in human resources, as it involves long and intricate computations. In recent years, we have seen increasing interest in using computer-based symbolic and algebraic manipulation for automatically generating numerical programs. Our Gradpack software uses as input a set of discrete equations (state equations) and formulas (cost functions) derived from a parameter estimation problem in a P.D.E's; the responsability of the discretization of the problem is left totally to the user: Gradpack knows only the resulting set of discrete equations and formulas - this allows a wider range of potential application for the software. Gradpack converts then these equations and formulas automatically into a set of Fortran codes for the computaton of the cost function and its gradients. The generated code should be used with a Fortran-based linear system analysis package and an optimization package. The optimization of generated code is studied.
Published Version
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