Estimation of Ordinary Differential Equation Models with Discretization Error Quantification
Year: 2021
Type: article
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.
DOI: 10.1137/19m1278405
Authors: Takeru Matsuda, Yuto Miyatake
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: Creation of a foundation for a numerical approach to deep learning, Parallel Structure-Preserving Algorithms: Theory and Numerical Verification, Statistical analysis of oscillation phenomenon in time series data, Development of Unified Numerical Methods for Large-Scale Matrix Functions in Physical and Information Sciences
OpenAlex ID: W2963736592