Open AccessThe spectral conjugate gradient method in variational adjoint assimilation for model terrain correction I: Theoretical frame
Author(s) -
Sulin Tao,
Yuhong Li,
Isaac Mugume,
Shuanghe Shen
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/768/7/072044
Subject(s) - conjugate gradient method , hessian matrix , regularization (linguistics) , uniqueness , gradient descent , mathematics , terrain , directional derivative , mathematical optimization , computer science , mathematical analysis , artificial neural network , ecology , artificial intelligence , machine learning , biology
A spectral conjugate gradient (SCG) method is proposed within the mathematical framework of a variational adjoint assimilation system to correct the bottom terrain of a shallow-water equations model. The formulation of this method is described from the mathematical point of view with determination of the descent direction by using Andrei’s limited-memory form and the step length by solving the tangent linear model. It is proved to benefit from (i) the iterative regularization strategy, (ii) the inverse Hessian approximation involving the second-order information from Broyden-Fletcher-Goldfarb-Shanno class (BFGS), and (iii) the optimal step length. The regularization term introduced to the cost function will allow the incorporation of the known information about the desired bottom terrain and guarantee the uniqueness of the optimal solution.