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