论文标题
分区runge的概括 - 伴随系统的kutta方法
Generalization of partitioned Runge--Kutta methods for adjoint systems
论文作者
论文摘要
这项研究计算了相对于初始条件的普通微分方程（ODE）数值解的功能的梯度。伴随方法通过数值求解相应的伴随系统来计算梯度。在这种情况下，Sanz-Serna [Siam Rev.，58（2016），第3---33页]表明，当通过runge-kutta（rk）方法解决初始值问题时，可以通过将适当的RK方法应用于相邻系统来精确计算梯度。重点关注通过分区RK（PRK）方法解决初始值问题的情况，本文提出了一种数值方法，可以将其视为PRK方法的概括，对于提供确切梯度的伴随系统。
This study computes the gradient of a function of numerical solutions of ordinary differential equations (ODEs) with respect to the initial condition. The adjoint method computes the gradient approximately by solving the corresponding adjoint system numerically. In this context, Sanz-Serna [SIAM Rev., 58 (2016), pp. 3--33] showed that when the initial value problem is solved by a Runge--Kutta (RK) method, the gradient can be exactly computed by applying an appropriate RK method to the adjoint system. Focusing on the case where the initial value problem is solved by a partitioned RK (PRK) method, this paper presents a numerical method, which can be seen as a generalization of PRK methods, for the adjoint system that gives the exact gradient.
