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Supported Methods for Parameter Estimation in SimBiology

SimBiology® supports a variety of optimization methods for least-squares and mixed-effects estimation problems. Depending on the optimization method, you can specify parameter bounds for estimated parameters as well as response-specific error models, that is, an error model for each response variable. The following table summarizes the supported optimization methods in SimBiology, fitting options, and the corresponding toolboxes that are required in addition to MATLAB® and SimBiology.

MethodAdditional Toolbox RequiredSupports Parameter BoundsUses Parameter SensitivitiesResponse-specific Error ModelsFixed or Mixed EffectsSupports Stochastic EM AlgorithmSimBiology Function to Use
fminsearchYes*NoYesFixedNosbiofit or fitproblem
scattersearchYesDepends on the selected local solver.Depends on the selected local solver.FixedNo
nlinfit (Statistics and Machine Learning Toolbox)Statistics and Machine Learning Toolbox™Yes*NoNoFixedNo
fminunc (Optimization Toolbox)Optimization Toolbox™Yes*YesYesFixedNo
fmincon (Optimization Toolbox)Optimization ToolboxYesYesYesFixedNo
lsqcurvefit (Optimization Toolbox)Optimization ToolboxYesYesYesFixedNo
lsqnonlin (Optimization Toolbox)Optimization ToolboxYesYesYesFixedNo
patternsearch (Global Optimization Toolbox)Global Optimization ToolboxYesNoYesFixedNo
ga (Global Optimization Toolbox)Global Optimization ToolboxYesNoYesFixedNo
particleswarm (Global Optimization Toolbox)Global Optimization ToolboxYesNoYesFixedNo
nlmefit (Statistics and Machine Learning Toolbox)Statistics and Machine Learning ToolboxNoNoNoMixedNosbiofitmixed or fitproblem
nlmefitsa (Statistics and Machine Learning Toolbox)Statistics and Machine Learning ToolboxNoNoNoMixedYes

This column indicates whether the algorithm allows using parameter sensitivities to determine gradients of the objective function.

* When using fminsearch, nlinfit, or fminunc with bounds, the objective function returns Inf if bounds are exceeded. When you turn on options such as FunValCheck, the optimization may error if bounds are exceeded during estimation. If using nlinfit, it may report warnings about the Jacobian being ill-conditioned or not being able to estimate if the final result is too close to the bounds.

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