EASY-FIT

Interactive parameter estimation for dynamic systems

EASY-FIT is an interactive software system to identify parameters in explicit model functions, dynamic systems of equations, Laplace transforms, ordinary differential equations, differential algebraic equations and one-dimensional time-dependent partial differential equations. Proceeding from given experimental data, i.e. observation times and measurements, the minimum least squares distances of measured data from a fitting criterion are computed, that may depend on the solution of the dynamic system. Four different optimization routines and seven different ODE-solvers are available and can be executed by EASY-FIT.

Some special features of EASY-FIT are:

  1. More than one fitting criterion may be defined, i.e. up to ten measurement sets are allowed.
  2. Fitting criteria may be arbitrary nonlinear model functions depending on the parameters to be estimated, and the solution of the dynamic subproblem.
  3. The mathematical model may possess arbitrary equality or inequality constraints depending on the parameters to be estimated, and also on the solution of the dynamic system.
  4. An additional independent model variable, e.g. defining a concentration, may be introduced.
  5. Model functions are either defined in form of a special language similar to FORTRAN, that allows symbolic interpretation of function values and their automatic differentiation, or alternatively in form of a user-provided FORTRAN routine.
  6. Switching points may be inserted where the integration is restarted to allow e.g. non-continous model changes. Switching points may become optimization parameters.
  7. Model functions may be defined by their Laplace transforms. The backtransformation is performed internally.

Constrained least squares problems can be solved by Gauss-Newton-type or related methods. Some alternative methods based on direct search are also available. Systems of nonlinear equations are solved by stabilized Newton method. Ordinary differential equations are integrated by a couple of explicit and implicit codes, also with internal numerical differentiation. Differential algebraic equations can be solved up to index 3. Consistent initial values for index 1 formulations are computed internally.

One-dimensional time-dependent partial differential equations are discretized w.r.t. spatial variable by polynomial approximation of arbitrary degree, difference formulae and special upwind formulae in case of hyperbolic equations. The approach is called the method of lines, i.e. the PDE is transformed into a system of ordinary differential equations. The resulting large and eventually stiff system of ordinary differential equations is solved by implicit integrators, where band structures are exploited. Nonlinear boundary and transition conditions between different areas, and coupled ordinary differential equations are allowed.

Typical practical applications of EASY-FIT are:

EASY-FIT is a user interface for the parameter estimation codes MODFIT, PDEFIT, and SYSFIT. All model functions, data and results are stored in a relational database implemented under MS- Access 8.0. A distribution-free runtime version of MS-Access is included. EASY-FIT requires MS-Windows 95/NT, at least 32 MB memory on board and about 42 MB on hard disk. Numerical algorithms are implemented as stand-alone executable files and can be used also outside of the database.

Model functions are either interpreted by the automatic differentiation tool PCOMP or provided by the user in form of FORTRAN code. In this case a FORTRAN compiler and linker must be available. Frames for executing the Watcom F77/386, the Salford FTN77, the Microsoft Fortran Powerstation or the Lahey F77 compiler are included. EASY-FIT comes with a full context sensitive help option and a handbook of about 200 pages that describes also the mathematical background. Data and function plots are generated either by the internal graphics system or alternatively by the external systems GNUPLOT, MS Graph 5.0 or Harvard ChartXL, if available, in 2D or 3D form.

A demo version is available on request containing all features of EASY-FIT with the restriction that model functions cannot be altered. A run-time version of MS-Access is included. The demo version is fully documented by interactive, context-sensitive help and comes with about 30 test examples, many of them based on real-life applications.

Need more info?

Take a look at the EASY-FIT home page (screen shots and download of demo version), or contact 

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

klaus.schittkowski@uni-bayreuth.de

Reference:

K. Schittkowski, Parameter estimation in systems of nonlinear equations, Numerische Mathematik, Vol. 68, 129--142 (1994).

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

M. Dobmann, M. Liepelt, K. Schittkowski, Algorithm 746: PCOMP: A FORTRAN code for automatic differentiation, ACM Transactions on Mathematical Software, Vol. 21, No. 3, 233-266 (1995).

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).

M. Dobmann, K. Schittkowski, PDEFIT: A FORTRAN code for constrained parameter estimation in partial differential equations, Report, Department of Mathematics, University of Bayreuth (1995)

K. Schittkowski, EASY-FIT: Parameter estimation in dynamical systems, User's Guide, Deptartment of Mathematics, University of Bayreuth (1996).

K. Schittkowski, Parameter estimation in one-dimensional time-dependent partial differential equations, Optimization Methods and Software, Vol. 7, No. 3-4, 165-210 (1997).

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