Numerical methods for computing sensitivities for ODEs and DDEs
Numerical methods for computing sensitivities for ODEs and DDEs
复制标题
计算 ODE 和 DDE 灵敏度的数值方法
作者：
J. Calver;W. Enright
我们调查的性能的伴随方法和变分方法计算的灵敏度最小二乘目标函数时，常用的拟合模型的观测。我们注意到，目标函数的离散性使得计算灵敏度的伴随方法的成本取决于观测的数量。在常微分方程（ODE）的情况下，这种依赖性是由于在伴随方程的数值解期间必须在每个观测点中断计算。每一个观测值在伴随微分方程的解中引入一个跳跃间断。这些不连续性传播的情况下，延迟微分方程（DDE），使伴随方法的性能更加敏感的观测DDE的数量。我们量化了这种成本，并提出了一些方法，使伴随方法的规模更好的观察。在数值实验中，我们比较了伴随方法和变分方法的灵敏度计算。
We investigate the performance of the adjoint approach and the variational approach for computing the sensitivities of the least squares objective function commonly used when fitting models to observations. We note that the discrete nature of the objective function makes the cost of the adjoint approach for computing the sensitivities dependent on the number of observations. In the case of ordinary differential equations (ODEs), this dependence is due to having to interrupt the computation at each observation point during numerical solution of the adjoint equations. Each observation introduces a jump discontinuity in the solution of the adjoint differential equations. These discontinuities are propagated in the case of delay differential equations (DDEs), making the performance of the adjoint approach even more sensitive to the number of observations for DDEs. We quantify this cost and suggest ways to make the adjoint approach scale better with the number of observations. In numerical experiments, we compare the adjoint approach with the variational approach for computing the sensitivities.