MODFIT

Parameter estimation in dynamic systems

MODFIT solves parameter estimation problems, where parameters in explicit model functions, Laplace transforms, systems of ordinary differential equations or systems of algebraic differential equations are to be identified. The problem may possess additional equality or inequality constraints.

The algorithm creates a nonlinear least squares problem and solves it by a couple of alternative parameter estimation methods, e.g. DFNLP. Differential equations can be integrated by seven available ODE-solvers, e.g. the Hairer and Wanner codes for stiff and non-stiff systems. If model functions are defined by thier Laplace transforms, the back-transformation performed by a formula of Stehfest. Gradients are evaluated either by numerical approximation or by internal numerical differentiation of a Runge-Kutta scheme.

Special features of MODFIT are

• more than one fitting criterion allowed,
• additional independent model variable (e.g. a concentration),
• switching points allow e.g. non-continous model changes, may become optimization variables,
• various scaling options,
• band structure can be exploited,
• multiple shooting for unstable equations,
• alternative direct search algorithms for parameter estimation, e.g. for problems with bad initial values,
• DAE's up to index 3,
• internal computation of consistent initial values for DAE's (index 1),
• generation of plot data and TEX-reports,
• full documentation,
• FORTRAN source code or executable code with interpretation of ASCII model file and automatic differentiation.

MODFIT are a double precision FORTRAN-77 subroutine and all parameters are passed through arguments. An additional main program takes over some organizational ballast and reads in all problem data. A user provided subroutine is required to define initial values, constraints, the right-hand side of a differential equation, or a fitting criterion. There exists a convenient user interface for MODFIT called EASY-FIT running under MS-Windows 95/NT.

Need more info?

Take a look at the author's home page, or contact

Prof. K. Schittkowski 
Dept. of Mathematics
University of Bayreuth 
95440 Bayreuth, Germany 

klaus.schittkowski@uni-bayreuth.de

Reference:

K. Schittkowski, MODFIT: A FORTRAN code for constrained parameter estimation in differential equations and explicit model functions, Report, Dept. of Mathematics, University of Bayreuth (1994).

K. Schittkowski, Parameter estimation in differential equations, in: Recent Trends in Optimization Theory and Applications, R.P. Agarwal ed., WSSIAA, World Scientific Publishing Co. (1995).

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