Parameter estimation in ODEs: assessing the potential of local and global solvers

M. Fernández de Dios, Á. M. González Rueda, J. R. Banga, J. González Díaz, D. R. Penas

In this work, we address parameter estimation in models described by nonlinear ordinary differential equations (ODEs) using a direct transcription approach. Controls and state profiles are discretized, leading to a nonlinear programming (NLP) problem solvable via mathematical programming techniques. The main goal of this work is to analyze the potential of mathematical modeling and state-of-the-art solvers to handle these problems. For this purpose, an extensive numerical study on eight challenging parameter estimation problems in nonlinear dynamic biological systems is carried out. Different modeling aspects, such as discretization schemes and formulation variants, are explored. The use of global and local solvers provides insights into local optimality and identifiability challenges. Our approach yields promising results, surpassing previously reported capabilities in the literature.

Keywords: Parameter estimation Dynamic modelling Optimization Mathematical programming

J. Bautista Valhondo

I. Izco Berastegui, A. Al-Rahamneh, A. Serrano Hernandez, J. Faulin Fajardo

A. Guerrero Portoles, M. Escoto Gomar, A. A. Juan, Á. García Sánchez, W. Chen