Forward and adjoint sensitivity analysis with continuous explicit Runge-Kutta schemes

被引:24
作者
Alexe, Mihai [1 ]
Sandu, Adrian [1 ]
机构
[1] Virginia Polytech Inst & State Univ, Dept Comp Sci, Sci Computat Lab, Blacksburg, VA 24060 USA
基金
美国国家科学基金会;
关键词
Sensitivity analysis; Dense output; Runge-Kutta pairs; Tangent linear models; Adjoint models; Automatic differentiation; DIFFERENTIAL-ALGEBRAIC EQUATIONS; CHEMICAL KINETIC SYSTEMS; AUTOMATIC DIFFERENTIATION; KPP; INTERPOLANTS;
D O I
10.1016/j.amc.2008.11.035
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study the numerical solution of tangent linear, first and second order adjoint models with high-order explicit, continuous Runge-Kutta pairs. The approaches currently implemented in popular packages such as SUNDIALS or DASPKADJOINT are based on linear multistep methods. For adaptive time integration of nonlinear models, interpolation of the forward model solution is required during the adjoint model simulation. We propose to use the dense output mechanism built in the continuous Runge-Kutta schemes as a highly accurate and cost-efficient interpolation method in the inverse problem run. We implement our approach in a Fortran library called DENSERKS, which is found to compare well to other similar software on a number of test problems. (C) 2008 Elsevier Inc. All rights reserved.
引用
收藏
页码:328 / 346
页数:19
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