Data Fitting Test Problems


1,300 test problems for parameter estimation (data fitting, system identification, nonlinear regression) in dynamical systems

The database of EASY-FIT (5.0)  contains now 1,300 test problems for data fitting in
- explicit model functions (243),
- steady state systems (41),
- Laplace transforms (10),
- ordinary differential equations (575),
- differential algebraic equations (62),
- one-dimensional, time-dependent partial differential equations (325),
- one-dimensional partial differential algebraic equations (44).
The problems can be used for testing
  1. data fitting software,
  2. least squares algorithms,
  3. ODE solvers,
  4. discretization methods for PDE's,
and for providing a large collection of mathematical models for direct inclusion in one's own projects. The problems are taken from literature or are by-products of cooperation with industrial and academic institutions. Among them are about 500 experimental data sets. The remaining ones are either simulated or predetermined 'by hand'.

Nonlinear model functions are implemented for the interpreter language PCOMP, which provides automatic differentiation features for computing first and second derivatives. There are two possibilities to execute the test problems from one's own software:
  1. The given text files are interpreted and available Fortran routines are called for computing function values and first or second derivatives.
  2. An available code generator is executed to produce Fortran code for function and gradient evaluation.
For more information read Algorithm 746: PCOMP: A FORTRAN code for automatic differentiation of M. Dobmann, M. Liepelt, and K. Schittkowski, published in ACM Transactions on Mathematical Software, Vol. 21, No. 3, 233-266 (1995). 
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