Estimation of ordinary differential equation models with discretization error quantification

TL;DR

This paper introduces a novel parameter estimation method for ODE models that explicitly quantifies discretization error, leading to more reliable and accurate estimates from noisy data.

Contribution

It develops an iterative reweighted least squares approach that models discretization error as random variables and estimates their variance alongside ODE parameters.

Findings

Achieves robust parameter estimation comparable to traditional methods.

Successfully quantifies discretization error to improve estimate reliability.

Demonstrates effectiveness through experimental validation.

Abstract

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