Parameter estimation of non-linear models using adjoint sensitivity analysis

Abstract

A problem of parameter estimation for non-linear models may be solved using different approaches, but in general cases it can be always transformed to an optimization problem. In such a case the minimized objective function is a measure of the discrepancy between the model solution and available measurements. This paper presents the ADFIT program — a tool for numerical parameter estimation for models that contain systems of non-linear ordinary differential equations. The user of the program provides a model in a symbolic form and the experimental data. The program utilizes adjoint sensitivity analysis to speed up gradient calculation of the quadratic objective function. The adjoint system generating the gradient is created automatically based on the symbolic form of the model. A numerical example of parameter estimation for a mathematical model arising in biology is also presented.