A variational approach to parameter estimation in ordinary differential equations

Supplement: A Variational Approach to Parameter Estimation in Ordinary Differential Equations

1 Parameter estimation in ODE systems with inputs Let ẏ = f(y, [x], p) (1) be an ODE for components y ∈ RN with continuous input function [x] ∈ C0(R,RM ). The system depends on dynamic parameters p ∈ RK and on initial conditions y(t = 0) which are combined to P = (p, y(t = 0)). The solution to eq. (1) is denoted by yP [x] and is a differentiable function of time t. Let us assume that the compon...

Parameter estimation of ordinary differential equations

This paper addresses the development of a new algorithm for parameter estimation of ordinary differential equations. Here, we show that (1) the simultaneous approach combined with orthogonal cyclic reduction can be used to reduce the estimation problem to an optimization problem subject to a fixed number of equality constraints without the need for structural information to devise a stable embe...

Convergence of the multistage variational iteration method for solving a general system of ordinary differential equations

In this paper, the multistage variational iteration method is implemented to solve a general form of the system of first-order differential equations. The convergence of the proposed method is given. To illustrate the proposed method, it is applied to a model for HIV infection of CD4+ T cells and the numerical results are compared with those of a recently proposed method.

Parameter Estimation for Differential Equations: A Gen- eralized Smoothing Approach

for instruction in the language and principles of chemical engineering, many consultations and much useful advice. Appreciation is also due to the referees, whose comments on an earlier version of the paper have been invaluable.

Parameter Estimation for Differential Equations