Opens the PottersWheel equalizer to change and to analyze
characteristics of the current fitting assembly.
The equalizer comprises several views:
- Plotting (Pl)
- Phase space (PS)
- Fitting (FV)
- Fit sequence analysis (N)
- Single fit analysis (1)
Eight pairs of sliders are available in th slider view to tune
selected parameters, with the left slider changing the
mantissa (fine tuning) and the right slider changing the
order of magnitude (coarse tuning). A parameter value can also be
entered directly into the textbox below the sliders.
The slider-pair on the left will be visible in each Equalizer view.
In order to keep parameters at a certain relationship, e.g.
a constant fraction of 3.0, a parameter equation can be applied, e.g.
kon = 3.0 * koff
If koff is changed, the value for kon is updated automatically and the
corresponding slider is set to its proper value. Please insert one equation
per line into the textbox on the right. To temporarilly turn off the
parameter equations, uncheck "Apply parameter equations".
The plotting view allows to show and hide a subset of variable of each
class u (driving inputs), x (dynamic variables), y (observables),
z (derived variables), and 'a' (algebraic expressions).
Please select a couple and variable class. The use the arrow buttons
between the listboxes "Visible" and "Invisible" to shift the selected
variables between the two sets.
It is often useful to plot several species into one subplot, e.g. to
directly compare their absolute values over time. This can be done by
creating variable groups. Afer selecting the species of interest click
on 'Create group' and provide an optional group name to identify the group
in the list of groups on the right and to specify the subplot header.
If the fitted model complies to the PottersWheel naming convention,
groups can be generated automatically by selecting the action
'Automatic group creation for basic species' and pressing 'Start action'.
Especially in large models the information content of the plotted
trajectories benefits from hiding all single variables and plotting only
In order to save or load a reasonable visualization setting select the
corresponding action and press 'Start action'. The generated file can
be copy-pasted into an existing model definition file in order to
start with a predefined visualization scheme from the beginning.
Not only variables but also stimuli can be made visible or invisible
Changes to the visualization setting take effect replotting the figures.
The phase space view allows to create pairs of two variables which will
be plotted against each other, i.e. in a so-called phase space diagramm.
The pairs are defined separately for each combined couple.
This view allows to plot the derivative of one variable x to a parameter k,
i.e. the sensitivity of x on k. This dependency is time-dependent and is
either approximated numerically or calculated during model integration by
suitable integrators based on analytical expressions. The latter approach
requires the CVODES integrator, the symbolic math toolbox, and the setting
config.integration.calcSensitivities = true
The fitting view allows to select an optimization strategy in normal
or logarithmic parameter space. The latter is recommended if you expect
model parameter to vary of orders of magnitude between each other or/and
during parameter calibration.
A single fit calibrates all non-fixed start values x0, dynamic parameters k,
and scaling (or observation) parameters s. Shortcut buttons exist to fit
only parameters from one of the three classes labeled 'x0', 'k', and 's'.
Fit sequences F2 and F3 with a specified number of fits 'n' and disturbance
strength 'd' can be run directly from the fitting view interface.
In this case calculation is accelerated by unchecking "Show fitting"
in order to avoid repetitive plotting of each fit.
Compare pwF2 and pwF3.
The boosted fit combines the trust region optimization with simulated
annealing in logarithmic and linear parameter space. This strategy is
a good starting point for a completely uncalibrated model. See pwFitBoost
for further information.
Which parameters are calibrated or stay fixed is usually defined in the
model definition files or the fit settings dialog. Temporarilly, parameters
may be fixed using the 'Set fixed pars' button.
Pressing the disturb button or running a fit sequence leads to varied
and refitted parameter values. The button 'Set disturbed pars.' allows
to define which parameters are disturbed. Compare pwDisturb and
A user-defined optimization function can be employed instead of the default
PottersWheel optimization strategy. This is done using the function
pwOptimizationSetUserFunction. By unchecking 'User fun', the user
optimization function may be quickly
turned off and on.
The following lists are used for fit-based analyses:
- Fit groups
- Fit sequences
- All fits
- Fits of analysis
Each fit is characterized by a fit group ID which represents
the fitted model-data-couples and set of calibrated parameters.
Additional fits under the same settings will receive the same
fit group ID. The list of fit groups displays the number of fits
in each group and their group ID. The function pwFitHistoryGetFits
may be used to access the fits group programmatically or to plot
Fits belonging to the same fit sequence are listed here characterized
by the time when the fit sequence started together with the number
of fits in the sequence.
To access an individual fit the list of all fits can be used.
Next to the start time of each fit, its chi-square value (CS)
is printed. One or more fits may be selected. When check-marking
the fields 'Direct plot' or 'Direct info', the system trajectories
or information of the fit are drawn or displayed, respectively,
when the fit gets selected.
Fits of analysis
When an analysis is carried out, e.g. a fit-sequence analysis
based on the best 50% of the fits with a minimum p-value of 0.01,
the resulting fits are displayed in the 'fits of analysis' list.
They can be saved into an xls or txt file using the menu
'Parameters | Save fits of analysis to file...'.
In the same fashion a set of fits may be loaded from a file
into the same list using the menu
'Parameters | Load fits of analysis from file...'.
Fit sequence analysis (N)
Several analyses exist to characterize subset of fit sequences:
- Linear fit sequence analysis
- Nonlinear Mean Optimal Transformation Approach (MOTA) analysis
- Scatter plots
Each analysis is applied to a subset of fits based on:
- Last fit sequence
- Selected fit sequence
- Selected fit group
- Selected fits
- Fits of (last) analysis
The subset is further constrained by
- Percentage of best fits
- A minimum p-value
- Percentage of included outliers
The subset of fits is ordered by the fit chi-square value.
By specifying a percentage of fits below 100, fits with the worst
fit quality are neglected.
A p-value is determined for each fit using a chi-square test for
N-#p degrees of freedom, where N is the number of fitted data points
and #p the number of calibrated parameters. All fits below the minimum
p-value are omitted.
It may be reasonable to determine the region in parameter
space where most of the fits are lying. Fits far away from this region,
i.e. outliers, should be excluded even if they have a similiar chi-square
The trajectories are displayed for each fit. Using the setting
config.optimization.levelOfHistoryStorage = 3;
when applying a fit allows to plot the saved trajectories
instead of fresh calculation. This is especially useful, if the
model trajectories are computationally expensive to be calculated.
The header of the PottersWheel equalizer displays information about the
|N||Number of fitted data points.|
|Chisq||Current chi-square value. Compare pwGoodnessOfFit.|
|Chisq/N||Chi-square value divided by N. Should be lower than 1 for a good fit.|
|D||Measure of deviation between true and fitted parameter values.|
|Only applies to fitting of simulated synthetic data.|