Estimation of ordinary differential equation models with discretization error quantification

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.

References in corpus (4)

• Sieve estimation of constant and time-varying coefficients in nonlinear ordinary differential equation models by considering both numerical error and measurement error
• Bayesian Probabilistic Numerical Methods
• Strong convergence rates of probabilistic integrators for ordinary differential equations
• Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Cited by in corpus (1)

• Randomised one-step time integration methods for deterministic operator differential equations