Estimating Unknown Time-Varying Parameters in Uncertain Differential Equation

TL;DR

This paper introduces a least squares estimation method for determining unknown time-varying parameters in uncertain differential equations, demonstrated through models of blood alcohol concentration and COVID-19.

Contribution

It extends existing methods by focusing on estimating time-varying parameters rather than constants in uncertain differential equations.

Findings

Successfully estimated time-varying parameters in blood alcohol and COVID-19 models.

Demonstrated the effectiveness of the method through regression fitting.

Provided a new approach for parameter estimation in uncertain differential equations.

Abstract

Uncertain differential equations have a wide range of applications. How to obtain estimated values of unknown parameters in uncertain differential equations through observations has always been a subject of concern and research, many methods have been developed to estimate unknown parameters. However, these parameters are constants. In this paper, the method of least squares estimation is recast for estimating the unknown time-varying parameters in uncertain differential equations. A set of unknown time-varying parameter estimates will be obtained, and then the unknown time-varying parameters will be obtained by regression fitting using the estimated values. Using this method, the uncertain differential equation of blood alcohol concentration in human body after drinking and the uncertain differential equation of COVID-19 are derived.