EASY-FIT ModelDesign 5.0

EASY-FIT ModelDesign 5.0 offers you a powerful tool to solve constrained nonlinear parameter estimation (nonlinear regression, data, curve and surface fitting) problems based on ODEs, DAEs, PDEs, PDAEs, steady-state systems, Laplace equations, and analytical functions. A statistical analysis provides confidence intervals, correlation and covariance matrix, identification of significant parameters, and allows optimum experimental design.

Interactive software system for parameter estimation and experimental design for dynamical systems based on:

• explicit model functions
• Laplace transforms
• steady state systems
• ordinary differential equations (ODE)
• differential algebraic equations (DAE)
• one-dimensional, time-dependent partial differential equations (PDE)
• one-dimensional, partial differential algebraic equations (PDAE)

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, which depends on the solution of the dynamic system. Various types of one-dimensional partial differential equations are permitted, also hyperbolic ones describing shock waves. Advection, diffusion, transport, or related equations can be solved successfully by non-oscillatory discretization schemes, even with non-continuous initial or boundary conditions.

A statistical analysis provides confidence intervals for estimated parameters, correlation and covariance matrix, identification of significance levels for estimated parameters, and optimum experimental design. As a by-product, curve and surface fits are available.

The software runs under MS-Windows Vista or XP, and a version for Windows 2K or earlier is available on request. For models based only on algebraic equations, see EASY-FIT Express. For minimizing any nonlinear functions subject to nonlinear constraints, see EASY-OPT Express. In both cases, a free download is offered.

Major Features:

1. User interface

• extensive database coming with 1.300 examples
• convenient modeling language with automatic differentiation
• alternative Fortran interface
• up to 30 fitting criteria and data sets
• syntax-highlighting editor
• extensive report and graphics facilities, also for Gnuplot
• in- and output of data by text files or Excel
• runs under Windows XP and Vista (contact the author for Windows 2K version)
  

2. General

• arbitrary fitting criteria depending on the parameters to be estimated, and the solution of the dynamic system
• additional nonlinear equality or inequality constraints
• second independent model variable called concentration
• switching points with restart of integration, e.g., for changing the model
• variable switching times, e.g.,  for modeling dynamical input functions
• alternative norms (sum of absolute values,  maximum of absolute values)
• confidence intervals for estimated parameters, correlation and covariance matrix
• identification of significance levels for estimated parameters
• computation of optimal experimental designs (A-criterion)
  

3. Ordinary differential equations (ODE)

• explicit and implicit solvers
• stiff and large ordinary differential equations, band structures
• shooting method for unstable ordinary differential equations
  

4. Ordinary differential algebraic equations (DAEs)

• algebraic equations up to index 3
• consistent index-1-initial values evaluated internally
  

5. One-dimensional, time-dependent partial differential equations (PDEs)

• coupled ordinary differential equations
• different integration areas with non-continuous transitions
• large number of discretization procedures
• upwind formulae and ENO method for hyperbolic equations
• boundary conditions in Dirichlet or Neumann form or as implicit algebraic equations
  

6. Database with 1.300 examples

• 243 explicit model functions
• 41 steady state systems
• 10 Laplace transforms
• 575 ordinary differential equations
• 62 differential algebraic equations
• 325 one-dimensional, time-dependent partial differential equations
• 44 one-dimensional partial differential algebraic equations

Benefits:

1. Solution of complex identification problems with minimal implementation efforts
2. Intuitively understandable and flexible modeling language
3. Huge number of test cases to start from
4. Sophisticated and up-to-date numerical routines
5. Sound scientific background
6. New and highly complex statistical tools (significance levels, optimum design)

WareSeeker Editor