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SystemModelParametricSimulate
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SystemModelParametricSimulate

[Experimental]

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SystemModelParametricSimulate[model,v,{p1,p2,…}]

simulates model for the variable v with parameters pi.

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SystemModelParametricSimulate[model,{v1,v2,…},{p1,p2,…}]

simulates model for multiple variables vi.

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SystemModelParametricSimulate[model,vars,tmax,…]

simulates from 0 to tmax.

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SystemModelParametricSimulate[model,vars,{tmin,tmax},…]

simulates from tmin to tmax.

Details and Options

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

Get a parametric solution for z with parameter a:

In[2]:=2
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https://wolfram.com/xid/01k3262tgy6lg7sic-sdzu7b
Out[2]=2

Evaluating with a numerical value of a gives an approximate function solution for z:

In[3]:=3
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https://wolfram.com/xid/01k3262tgy6lg7sic-83thhh
Out[3]=3

Evaluate at a time t=10:

In[4]:=4
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https://wolfram.com/xid/01k3262tgy6lg7sic-ggz0d3
Out[4]=4

Plot the solutions for several different values of the parameter:

In[5]:=5
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https://wolfram.com/xid/01k3262tgy6lg7sic-xl62tf
Out[5]=5

Get a parametric solution for z with respect to the initial value of y:

In[1]:=1
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https://wolfram.com/xid/01k3262tgy6lg7sic-6rbhgc
Out[1]=1

Plot the solutions for several different values of the parameter:

In[2]:=2
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https://wolfram.com/xid/01k3262tgy6lg7sic-rjj4c7
Out[2]=2

Show the sensitivity of the variable z to the parameter a:

In[1]:=1
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https://wolfram.com/xid/01k3262tgy6lg7sic-hv2xlj
Out[1]=1

The sensitivity with respect to a increases with time:

In[2]:=2
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https://wolfram.com/xid/01k3262tgy6lg7sic-ztqxyx
Out[2]=2

Scope  (4)Survey of the scope of standard use cases

Models  (4)

Get a parametric solution for variables in a SystemModel with respect to a parameter:

In[1]:=1
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https://wolfram.com/xid/01k3262tgy6lg7sic-bb1mgg
Out[1]=1

Plot the solutions for several different values of the parameter:

In[2]:=2
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https://wolfram.com/xid/01k3262tgy6lg7sic-yezz5t
Out[2]=2

Get a parametric solution for a variable in an AffineStateSpaceModel with respect to a parameter:

In[1]:=1
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https://wolfram.com/xid/01k3262tgy6lg7sic-jcndlr
Out[1]=1

Plot the solutions for several different values of the parameter:

In[2]:=2
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https://wolfram.com/xid/01k3262tgy6lg7sic-vx83cy
Out[2]=2

Get a parametric solution for a variable in a NonlinearStateSpaceModel with respect to a parameter:

In[1]:=1
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https://wolfram.com/xid/01k3262tgy6lg7sic-iw0ekq
Out[1]=1

Plot the solutions for several different values of the parameter:

In[2]:=2
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https://wolfram.com/xid/01k3262tgy6lg7sic-wvhp9y
Out[2]=2

Get a parametric solution for a variable in a DiscreteInputOutputModel with respect to a parameter:

In[1]:=1
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https://wolfram.com/xid/01k3262tgy6lg7sic-9br5lt
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/01k3262tgy6lg7sic-e4lmem
Out[2]=2

Plot the solutions for several different values of the parameter:

In[3]:=3
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https://wolfram.com/xid/01k3262tgy6lg7sic-q2oht8
Out[3]=3

Options  (1)Common values & functionality for each option

Method  (1)

Use Method to choose the underlying solver:

In[1]:=1
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https://wolfram.com/xid/01k3262tgy6lg7sic-hp6ksz

Use the DASSL solver:

In[2]:=2
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https://wolfram.com/xid/01k3262tgy6lg7sic-3stp62
Out[2]=2

Use ParametricNDSolve as the solver:

In[3]:=3
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https://wolfram.com/xid/01k3262tgy6lg7sic-mi4jzl
Out[3]=3

ParametricNDSolve is often faster than other solvers:

In[4]:=4
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https://wolfram.com/xid/01k3262tgy6lg7sic-9oyhlu
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/01k3262tgy6lg7sic-n7bk7e
Out[5]=5

Applications  (2)Sample problems that can be solved with this function

Optimize parameters for maximizing a throw by a trebuchet:

In[14]:=14
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https://wolfram.com/xid/01k3262tgy6lg7sic-zdhl22

Retrieve a parametric function for the thrown distance, varying release time and rope length:

In[15]:=15
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https://wolfram.com/xid/01k3262tgy6lg7sic-use35b
Out[15]=15

Maximize the throwing distance, constraining parameters to reasonable ranges:

In[4]:=4
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https://wolfram.com/xid/01k3262tgy6lg7sic-e6dmob
Out[4]=4

Simulate using the optimal throwing parameters:

In[5]:=5
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https://wolfram.com/xid/01k3262tgy6lg7sic-yqhwiq
Out[5]=5

Show the distance until the first bounce:

In[6]:=6
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https://wolfram.com/xid/01k3262tgy6lg7sic-ht3rrd
Out[6]=6

Plot the trajectory of the thrown object using a stored plot:

In[7]:=7
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https://wolfram.com/xid/01k3262tgy6lg7sic-e4v3co
Out[7]=7

Calibrate parameters in a model by comparing to measurement data:

In[1]:=1
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https://wolfram.com/xid/01k3262tgy6lg7sic-eirvkk

Compute a parametric function for the inertia variable measured:

In[2]:=2
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https://wolfram.com/xid/01k3262tgy6lg7sic-tkfwwq
Out[2]=2

Set up a criteria function for model fitting:

In[3]:=3
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https://wolfram.com/xid/01k3262tgy6lg7sic-zeq44

Fit parameters to the test data:

In[4]:=4
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https://wolfram.com/xid/01k3262tgy6lg7sic-ci2f7k
Out[4]=4

Simulate with the fitted parameters:

In[5]:=5
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https://wolfram.com/xid/01k3262tgy6lg7sic-qefb4x

Show the test data and the calibrated model together:

In[6]:=6
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https://wolfram.com/xid/01k3262tgy6lg7sic-g6m480
Out[6]=6

Properties & Relations  (1)Properties of the function, and connections to other functions

SystemModelSimulateSensitivity can be used to easily compute parameter sensitivity:

In[1]:=1
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https://wolfram.com/xid/01k3262tgy6lg7sic-1y7734

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

In[2]:=2
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https://wolfram.com/xid/01k3262tgy6lg7sic-3v339w
Out[2]=2
Wolfram Research (2018), SystemModelParametricSimulate, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemModelParametricSimulate.html (updated 2022).
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Wolfram Research (2018), SystemModelParametricSimulate, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemModelParametricSimulate.html (updated 2022).

Text

Wolfram Research (2018), SystemModelParametricSimulate, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemModelParametricSimulate.html (updated 2022).

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Wolfram Research (2018), SystemModelParametricSimulate, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemModelParametricSimulate.html (updated 2022).

CMS

Wolfram Language. 2018. "SystemModelParametricSimulate." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/SystemModelParametricSimulate.html.

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Wolfram Language. 2018. "SystemModelParametricSimulate." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/SystemModelParametricSimulate.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2025_systemmodelparametricsimulate, author="Wolfram Research", title="{SystemModelParametricSimulate}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/SystemModelParametricSimulate.html}", note=[Accessed: 30-March-2025 ]}

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@misc{reference.wolfram_2025_systemmodelparametricsimulate, author="Wolfram Research", title="{SystemModelParametricSimulate}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/SystemModelParametricSimulate.html}", note=[Accessed: 30-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_systemmodelparametricsimulate, organization={Wolfram Research}, title={SystemModelParametricSimulate}, year={2022}, url={https://reference.wolfram.com/language/ref/SystemModelParametricSimulate.html}, note=[Accessed: 30-March-2025 ]}

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@online{reference.wolfram_2025_systemmodelparametricsimulate, organization={Wolfram Research}, title={SystemModelParametricSimulate}, year={2022}, url={https://reference.wolfram.com/language/ref/SystemModelParametricSimulate.html}, note=[Accessed: 30-March-2025 ]}