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.
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
- SystemModelSimulateSensitivity is used to estimate the variations in simulation results when changing parameter values in system models.
- The model can have the following forms:
-
- SystemModelSimulateSensitivity returns a SystemModelSimulationData object.
- For a SystemModel model, SystemModelSimulateSensitivity generates solutions for all variables , as well as derivatives , , … for all states , for .
- For other types of models, SystemModelSimulateSensitivity generates solutions for all variables , as well as derivatives , , …, for .
- Sensitivities can be listed in a SystemModelSimulationData object sd with sd["SensitivityNames"].
- The stored simulation variables vars can have the following values:
-
Automatic automatically choose what to store{v1,v2,…} store only variables viAll store all variables
- SystemModelSimulateSensitivity […,spec] uses Association spec for initial values, parameters and inputs:
-
"ParameterValues" {p1val1,…} parameter pi has value vali"InitialValues" {v1val1,…} variable vi has initial value vali"Inputs" {in1fun1,…} input ini has value funi[t] at time t
- Setting "ParameterValues" or "InitialValues" to {pi->{c1,c2,…},…} runs simulations in parallel, with pi taking values cj.
- "InitialValues" corresponds to the start property in the Modelica model.
- The following options can be given:
-
- The option setting Automatic normally means that the setting is taken from model or its experiment setting.
- For a SystemModel model, the CVODES solver used can be controlled with Method->{"opt1"->val1}.
- Possible suboptions for the CVODES method include:
-
"InterpolationPoints" Automatic number of interpolation points"Tolerance" 10-6 tolerance for adaptive step size
Examples
open all close allBasic 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:
Related Guides
Related Links
History
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: 18-November-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: 18-November-2025]}