SystemModelSimulateSensitivity

SystemModelSimulateSensitivity[model,{p1,p2,…}]

simulates model and sensitivities to parameters pi following experiment settings.

SystemModelSimulateSensitivity[model,tmax,{p1,p2,…}]

simulates from 0 to tmax.

SystemModelSimulateSensitivity[model,{tmin,tmax},{p1,p2,…}]

simulates from tmin to tmax.

SystemModelSimulateSensitivity[model,vars,{tmin,tmax},{p1,p2,…}]

stores only simulation data for the variables vars.

Details and Options

Examples

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Basic Examples  (3)

Study sensitivity of a parameter over the time interval in model experiment settings:

Extract sensitivity names and plot them:

Show the sensitivity of a signal to relative changes in a parameter:

Plot bounds for y and z when varying a by 10%:

Use the diagram representation of a model as input:

Copy and paste the output above:

Scope  (16)

Models  (3)

Compute variables and sensitivities when simulating a NonlinearStateSpaceModel:

Extract sensitivity names and plot them:

Plot bounds for a state when varying a by 40%:

Compute sensitivities in a parameter sweep for an AffineStateSpaceModel:

Plot bounds for a state when varying a by 50%:

Compute sensitivities for a DiscreteInputOutputModel:

Plot bounds for the output when varying a by 5%:

Simulation Time  (3)

Simulate with settings from the model:

Simulate from time 0 to 5:

Simulate for an explicit time interval:

Sensitivity Results  (6)

Study the sensitivity of one parameter:

Simulate with sensitivity to parameter a:

Get the sensitivity names:

Get the sensitivity y has to changes in a:

Study the sensitivities from one parameter:

Plot one of the sensitivities:

Show the sensitivity of a signal to a parameter a:

Get the sensitivity names:

Get the sensitivity y has to changes in a, as well as the nominal trajectory for y:

Plot y with original parameter a, and with parameter a increased by 0.05:

Show the sensitivity of a signal to relative changes in a parameter:

Get the sensitivity names:

Get the sensitivity y and z have to changes in a, as well as nominal trajectories and value:

Plot bounds for y and z when varying a by 10% of the sensitivity:

Show the sensitivity of a signal to absolute changes in a parameter a:

Get the sensitivity y has to changes in a, as well as the trajectory for y:

Compute the change in y when parameter a changes with absolute value 0.1:

Plot the variation of y when parameter a varies by ±0.1:

Variables, Parameters and Inputs  (3)

Change the initial values of a simulation:

Compare the changes in a plot:

Change the parameter values of a simulation:

Compare the two in a plot:

Give an input function for a variable and study the sensitivity of the output to a gain parameter:

Plot the sensitivity of the output to the gain parameter:

Result Storage  (1)

Store only selected variables:

Only the given variables and parameters are saved:

Generalizations & Extensions  (1)

Debug messages are collected in the message group "WSMDebug":

Turn on debug messages for initialization:

Turn off all debug messages for "WSMDebug":

Options  (3)

InterpolationOrder  (1)

Simulate with interpolation orders 1 and 3, and 3 interpolation points:

Show the sensitivity variable:

Method  (1)

Simulate a SystemModel and compute sensitivities with the number of interpolation points set by the model:

Simulate and compute sensitivities with a custom number of interpolation points:

ProgressReporting  (1)

Control progress reporting with ProgressReporting:

Applications  (5)

Study the sensitivity of a model:

Get the value of the parameter:

Find the peak deviation when varying the parameter:

Show a 5% sensitivity bound and the peak deviation time:

Find out which variable is most sensitive to a frequency parameter:

A 10% sensitivity bound shows that "integrator3.y" is most sensitive to the parameter:

Simulate a rolling wheel:

Select the position of the wheel and its sensitivities to different parameters:

Show the path of the wheel with 4% variation of the wheel radius and mass, respectively:

Calibrate parameters in a model by comparing to measurement data:

Set up caching for simulation:

Use SystemModelSimulateSensitivity to get gradients:

Plot the result of the simulation for specific parameter values:

Fit parameters to the measurement data:

Not using gradients takes longer:

Simulate with the fitted parameters:

Show the test data and the calibrated model together:

Plot a solution with its sensitivity bounds:

Get the nominal value of the parameter:

Show a 5% sensitivity bound:

Simulate with a maximal variation of 5%:

Get the trajectories:

Show that the trajectories are mostly contained in the approximated sensitivity bounds:

Properties & Relations  (4)

Compare a sensitivity simulation with the sensitivity of the corresponding differential equation:

Plot bounds for a relative parameter change:

Get the sensitivity y has to changes in a, as well as y and the value for a:

Plot bounds for y when varying a by 10% of the sensitivity:

Use SystemModelPlot instead:

Sensitivities are valid for small changes in the parameter:

Get sensitivities to a parameter:

Simulate with variation of the parameter:

Comparing in a plot, a 10% variation gives trajectories outside computed bounds:

Use SystemModelParametricSimulate for a function that can be evaluated for different values:

Compute solutions for different values of the frequency parameter:

Plot the solutions over time:

Neat Examples  (1)

Show sensitivity bounds for the and axes in the Rabinovich–Fabrikant equations:

Show the sensitivity bounds in 3D:

Wolfram Research (2018), SystemModelSimulateSensitivity, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemModelSimulateSensitivity.html.

Text

Wolfram Research (2018), SystemModelSimulateSensitivity, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemModelSimulateSensitivity.html.

CMS

Wolfram Language. 2018. "SystemModelSimulateSensitivity." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SystemModelSimulateSensitivity.html.

APA

Wolfram Language. (2018). SystemModelSimulateSensitivity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SystemModelSimulateSensitivity.html

BibTeX

@misc{reference.wolfram_2025_systemmodelsimulatesensitivity, author="Wolfram Research", title="{SystemModelSimulateSensitivity}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/SystemModelSimulateSensitivity.html}", note=[Accessed: 16-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_systemmodelsimulatesensitivity, organization={Wolfram Research}, title={SystemModelSimulateSensitivity}, year={2018}, url={https://reference.wolfram.com/language/ref/SystemModelSimulateSensitivity.html}, note=[Accessed: 16-May-2025 ]}