Estimation of Ordinary Differential Equation Models with Discretization Error Quantification

We consider parameter estimation of ordinary differential equation (ODE) models from noisy observations. For this problem, one conventional approach is to fit numerical solutions (e.g., Euler, Runge--Kutta) ODEs data. However, such a method does not account for the discretization error in and has limited accuracy. In study, we develop an that quantifies based on The key idea model as random variables estimate their variance simultaneously with ODE parameter. proposed form iteratively reweighted least squares, where updated isotonic regression algorithm by solving weighted squares problem using adjoint system. Experimental results demonstrate attains robust at comparable accuracy successfully quantifying reliability solutions.