TY - GEN

T1 - Numerical Comparison of the Adjoint Problem-based and Derivative-free Algorithms on the Coefficient Identification Problem for a Production-Loss Model

AU - Penenko, Alexey

AU - Konopleva, Viktoria

AU - Bobrovskikh, Aleksandr

N1 - Funding Information: Supported by RFBR 19-07-01135 (inverse coefficient problem with point-wise data) and RFBR 19-44-543021 (biological model) Publisher Copyright: © 2021 IEEE

PY - 2021

Y1 - 2021

N2 - Coefficient identification problems for non-stationary production-loss models are considered. Such models are widely used in chemical, environmental, economic, and biological process studies. The objective of the work is to numerically compare standard derivative-free and gradient-based optimization algorithms accuracy to that of the algorithm consisting of solving the quasi-linear matrix equation with the sensitivity operator. The matrix equation is solved by means of the Newton-Kantorovich-type algorithm with the truncated SVD regularized matrix inversion. Both gradient and sensitivity operator-based algorithms use adjoint problems. The algorithms are compared on the inverse modeling scenario for the antioxidant system of a plant cell. In the scenario, the parameters of the model with rational production-loss operators have to be identified by the state function measurements with the regular time steps. In the numerical experiments, the adjoint problem-based algorithms showed almost the same accuracy, while derivative-free algorithms were less accurate. The largest errors of the latter were obtained on the model coefficients that were not identified by the adjoint problem-based algorithms.

AB - Coefficient identification problems for non-stationary production-loss models are considered. Such models are widely used in chemical, environmental, economic, and biological process studies. The objective of the work is to numerically compare standard derivative-free and gradient-based optimization algorithms accuracy to that of the algorithm consisting of solving the quasi-linear matrix equation with the sensitivity operator. The matrix equation is solved by means of the Newton-Kantorovich-type algorithm with the truncated SVD regularized matrix inversion. Both gradient and sensitivity operator-based algorithms use adjoint problems. The algorithms are compared on the inverse modeling scenario for the antioxidant system of a plant cell. In the scenario, the parameters of the model with rational production-loss operators have to be identified by the state function measurements with the regular time steps. In the numerical experiments, the adjoint problem-based algorithms showed almost the same accuracy, while derivative-free algorithms were less accurate. The largest errors of the latter were obtained on the model coefficients that were not identified by the adjoint problem-based algorithms.

KW - adjoint equations

KW - coefficient identification

KW - derivative-free algorithms

KW - gradient-based methods

KW - production-loss models

KW - sensitivity operator

UR - http://www.scopus.com/inward/record.url?scp=85126971490&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/4b07cc3f-bd7e-3523-a9f3-ac9e01722375/

U2 - 10.1109/OPCS53376.2021.9588680

DO - 10.1109/OPCS53376.2021.9588680

M3 - Conference contribution

AN - SCOPUS:85126971490

SN - 9781665405621

T3 - Proceedings - 2021 17th International Asian School-Seminar "Optimization Problems of Complex Systems", OPCS 2021

SP - 78

EP - 83

BT - Proceedings - 2021 17th International Asian School-Seminar "Optimization Problems of Complex Systems", OPCS 2021

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 17th International Asian School-Seminar "Optimization Problems of Complex Systems", OPCS 2021

Y2 - 13 September 2021 through 17 September 2021

ER -