Comparing nonlinear optimization techniques to predict dynamic parameters of biological processes in nonlinear differential equation models

Abstract

The modeling of nonlinear dynamics, which has been a significant research topic for half a decade. During the development process, the modeler creates a model that is as close to the underlying real dynamics as possible. It is extremely difficult to evaluate the numerous parameters that appear in the nonlinear equations in a way that does not cause the parameter estimates of the dynamic constants to stray into regions of parameter space that produce nonphysical predictions. The use of parameter estimation and nonlinear fitting techniques in conjunction with numerical models allows for greater flexibility by allowing for a variety of experimental boundary and starting conditions. The majority of the defined methods are iterative in nature, necessitating the use of an initial estimate of the unknown parameters to be optimized before proceeding. Multi-objective optimization methods are also used to capture both the underlying dynamics and the main response. Although it is possible to estimate unknown parameters in complex nonlinear differential equation models using experimental or clinical data, doing so is extremely difficult. Consequently, we usually fix some parameter values, either based on literature or personal experience, in order to obtain only parameter estimates that are relevant from clinical or experimental data. When such prior information is not available, it is preferable to derive all of the parameter estimates from data rather than from prior information. In this study, different nonlinear optimization approaches will be compared in order to estimate different biological dynamic parameters in a nonlinear differential equation model.