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Running PEST
5-26
If PEST does not lower the objective function, or lowers it slowly, you should run through the
following checklist of reasons for PEST’s poor performance. In most instances the problem
can be rectified.
5.5.2 Derivatives are not Calculated with Sufficient Precision
Precise calculation of derivatives is critical to PEST’s performance. Improper derivatives
calculation will normally be reflected in an inability on the part of PEST to achieve full
convergence to the optimal parameter set. Sometimes, in such circumstances, PEST will
commence an optimisation run in spectacular fashion, lowering the objective function
dramatically in the first optimisation iteration or two. But then it “runs out of steam”, failing
to lower it much further.
Make sure that model outcomes are being written to the model output file with the maximum
precision which the model allows. If the model places an upper limit on output precision,
ensure that the parameter increments used for derivatives calculation are large enough to
cause a useable change in all model-calculated observations, given the number of significant
digits in which they are expressed. Try not to make parameter increments too large though, or
finite-difference-generated derivatives will be a poor approximation to the real thing.
However if they must be large, use one of the three-point methods of derivatives calculation.
Try the “parabolic” method first; if that doesn't work, use the “best-fit” method.
Check that parameter values are written to model input files with enough significant digits to
reflect parameter increments. If some parameters become very low as the optimisation
process progresses, you may need to provide a suitable lower bound on derivative increments
through the parameter group variable DERINCLB, or calculate the increment using the
largest member of a parameter group by denoting the group variable INCTYP as
“rel_to_max”.
For a model which solves large matrix equations using an iterative method, you should ensure
that the model’s solution convergence criterion is set very low so that model-generated
observations are calculated with a high degree of precision. However if you set it too low the
model solution procedure may not converge; worse still, it may converge for some parameter
sets and not for others. To overcome this you may need to make a small change to the model
such that it prints out its solution vector even if it has not converged according to your very
stringent convergence setting; alternatively you could employ a batch process such as was
demonstrated in Example 4.3.
5.5.3 High Parameter Correlation
There is often a temptation in fitting models to data, to improve the fit between modelled and
measured observations by increasing the number of adjustable parameters. While it is true
that this can result in a lowered objective function, it is not always true that such an
improvement increases a model’s ability to make reliable predictions, or that a high number
of parameters represents a valid interpretation of the dataset to which the model’s outcomes
are matched. Furthermore, as the number of parameters requiring estimation is increased,
there will come a stage where PEST’s ability to lower the objective function by adjusting the
values of these parameters is diminished due to the effects of roundoff error (particularly for
highly nonlinear models); this applies not just to PEST but to any parameter estimation