Program to estimate parameters of linear systems without numerical differentiation

Area of Science:

• Computational Mathematics
• Systems Biology
• Parameter Estimation

Background:

• Estimating parameters in linear differential equations with constant coefficients is crucial for modeling dynamic systems.
• Traditional methods can suffer from inaccuracies introduced by numerical differentiation.
• Developing robust and efficient parameter estimation techniques is an ongoing challenge.

Purpose of the Study:

• To describe a novel computer program for parameter estimation in linear differential equation systems.
• To implement a nonlinear least-squares method combined with Taylor expansion for improved accuracy.
• To eliminate the need for numerical differentiation in parameter estimation.

Main Methods:

• A nonlinear least-squares method was employed for parameter estimation.
• The Gauss-Newton gradient procedure was utilized for minimization.
• The differential equation system was solved using the Taylor expansion method, providing analytical derivatives.

Main Results:

• The developed program successfully estimates parameters for linear differential equation systems.
• The Taylor expansion method eliminates the need for numerical differentiation, avoiding associated inaccuracies.
• The method demonstrated effectiveness when tested with data from a four-compartmental model.

Conclusions:

• The presented computer program offers an accurate and efficient approach to parameter estimation for linear differential equations.
• This method enhances the reliability of parameter estimation by avoiding numerical differentiation.
• The approach is broadly applicable to first-order gradient methods and complex models.