ModelingToolkit Language: Modeling with @mtkmodel, @connectors and @mtkcompile

MTK Model

MTK represents components and connectors with Model.

struct Model{F, S}

Components

Components are models from various domains. These models contain unknowns and their equations.

Defining components with @mtkmodel

@mtkmodel is a convenience macro to define components. It returns ModelingToolkit.Model, which includes a system constructor (System by default), a structure dictionary with metadata, and flag isconnector which is set to false.

What can an MTK-Model definition have?

@mtkmodel definition contains begin blocks of

• @description: for describing the whole system with a human-readable string
• @components: for listing sub-components of the system
• @constants: for declaring constants
• @defaults: for passing defaults to the system
• @equations: for the list of equations
• @extend: for extending a base system and unpacking its unknowns
• @icon : for embedding the model icon
• @parameters: for specifying the symbolic parameters
• @structural_parameters: for specifying non-symbolic parameters
• @variables: for specifying the unknowns
• @continuous_events: for specifying a list of continuous events
• @discrete_events: for specifying a list of discrete events

Let's explore these in more detail with the following example:

using ModelingToolkit
using ModelingToolkit: t

@mtkmodel ModelA begin
    @description "A component with parameters `k` and `k_array`."
    @parameters begin
        k
        k_array[1:2]
    end
end

@mtkmodel ModelB begin
    @description "A component with parameters `p1` and `p2`."
    @parameters begin
        p1 = 1.0, [description = "Parameter of ModelB"]
        p2 = 1.0, [description = "Parameter of ModelB"]
    end
end

@mtkmodel ModelC begin
    @description "A bigger system that contains many more things."
    @icon "https://github.com/SciML/SciMLDocs/blob/main/docs/src/assets/logo.png"
    @constants begin
        c::Int = 1, [description = "Example constant."]
    end
    @structural_parameters begin
        f = sin
        N = 2
        M = 3
    end
    begin
        v_var = 1.0
    end
    @variables begin
        v(t) = v_var
        v_array(t)[1:N, 1:M]
        v_for_defaults(t)
    end
    @extend ModelB(p1 = 1)
    @components begin
        model_a = ModelA(; k_array)
        model_array_a = [ModelA(; k = i) for i in 1:N]
        model_array_b = for i in 1:N
            k = i^2
            ModelA(; k)
        end
    end
    @equations begin
        model_a.k ~ f(v)
    end
    @defaults begin
        v_for_defaults => 2.0
    end
end

ModelingToolkit.Model{typeof(Main.var"Main".__ModelC__), Dict{Symbol, Any}}(Main.var"Main".__ModelC__, Dict{Symbol, Any}(:description => "A bigger system that contains many more things.", :variables => Dict{Symbol, Dict{Symbol, Any}}(:v => Dict(:default => :v_var, :type => Real), :v_array => Dict(:value => nothing, :type => Real, :size => (:N, :M)), :v_for_defaults => Dict(:type => Real)), :structural_parameters => Dict{Symbol, Dict}(:f => Dict(:value => :sin), :N => Dict(:value => 2), :M => Dict(:value => 3)), :extend => Any[[:p2, :p1], Symbol("#mtkmodel__anonymous__ModelB"), :ModelB], :equations => Any["model_a.k ~ f(v)"], :icon => URI("https://github.com/SciML/SciMLDocs/blob/main/docs/src/assets/logo.png"), :independent_variable => :t, :constants => Dict{Symbol, Dict{Symbol, Any}}(:c => Dict(:default => 1, :type => Int64, :description => "Example constant.")), :defaults => Dict{Symbol, Any}(:v_for_defaults => 2.0), :components => Any[Union{Expr, Symbol}[:model_a, :ModelA], Union{Expr, Symbol}[:model_array_a, :ModelA, :(1:N)], Union{Expr, Symbol}[:model_array_b, :ModelA, :(1:N)]]…), false)

@description

A documenting String that summarizes and explains what the model is.

@icon

An icon can be embedded in 3 ways:

• URI
• Path to a valid image-file.<br> It can be an absolute path. Or, a path relative to an icon directory; which is DEPOT_PATH[1]/mtk_icons by default and can be changed by setting ENV["MTK_ICONS_DIR"].<br> Internally, it is saved in the File URI scheme.

@mtkmodel WithPathtoIcon begin
    @icon "/home/user/.julia/dev/mtk_icons/icon.png"
    # Rest of the model definition
end

• Inlined SVG.

@mtkmodel WithInlinedSVGIcon begin
    @icon """<svg height="100" width="100">
    <circle cx="50" cy="50" r="40" stroke="green" fill="none" stroke-width="3"/>
    </svg>
    """
    # Rest of the model definition
end

@structural_parameters begin block

• This block is for non symbolic input arguments. These are for inputs that usually are not meant to be part of components; but influence how they are defined. One can list inputs like boolean flags, functions etc... here.
• Whenever default values are specified, unlike parameters/variables, they are reflected in the keyword argument list.

@constants begin block

• Declare constants in the model definition.
• The values of these can't be changed by the user.
• This works similar to symbolic constants described here

@parameters and @variables begin block

• Parameters and variables are declared with respective begin blocks.
• Variables must be functions of an independent variable.
• Optionally, initial guess and metadata can be specified for these parameters and variables. See ModelB in the above example.
• Along with creating parameters and variables, keyword arguments of same name with default value nothing are created.
• Whenever a parameter or variable has initial value, for example v(t) = 0.0, a symbolic variable named v with initial value 0.0 and a keyword argument v, with default value nothing are created. <br> This way, users can optionally pass new value of v while creating a component.

julia> @mtkcompile model_c1 = ModelC(; v = 2.0);

julia> ModelingToolkit.getdefault(model_c1.v)
2.0

@extend statement

One or more partial systems can be extended in a higher system with @extend statements. This can be done in two ways:

• @extend PartialSystem(var1 = value1)

  • This is the recommended way of extending a base system.
  • The default values for the arguments of the base system can be declared in the @extend statement.
  • Note that all keyword arguments of the base system are added as the keyword arguments of the main system.

• @extend var_to_unpack1, var_to_unpack2 = partial_sys = PartialSystem(var1 = value1)

  • In this method: explicitly list the variables that should be unpacked, provide a name for the partial system and declare the base system.
  • Note that only the arguments listed out in the declaration of the base system (here: var1) are added as the keyword arguments of the higher system.

@components begin block

• Declare the subcomponents within @components begin block.
• Array of components can be declared with a for loop or a list comprehension.
• The arguments in these subcomponents are promoted as keyword arguments as subcomponent_name__argname with nothing as default value.
• Whenever components are created with @named macro, these can be accessed with . operator as subcomponent_name.argname
• In the above example, as k of model_a isn't listed while defining the sub-component in ModelC, its default value can't be modified by users. While k_array can be set as:

using ModelingToolkit: getdefault

@mtkcompile model_c3 = ModelC(; model_a.k_array = [1.0, 2.0])

getdefault(model_c3.model_a.k_array[1])
# 1.0
getdefault(model_c3.model_a.k_array[2])
# 2.0

2.0

@equations begin block

• List all the equations here

@defaults begin block

• Default values can be passed as pairs.
• This is equivalent to passing defaults argument to the system.

@continuous_events begin block

• Defining continuous events as described here.
• If this block is not defined in the model, no continuous events will be added.
• Discrete parameters and other keyword arguments should be specified in a vector, as seen below.

using ModelingToolkit
using ModelingToolkit: t

@mtkmodel M begin
    @parameters begin
        k(t)
    end
    @variables begin
        x(t)
        y(t)
    end
    @equations begin
        x ~ k * D(x)
        D(y) ~ -k
    end
    @continuous_events begin
        [x ~ 1.5] => [x ~ 5, y ~ 5]
        [t ~ 4] => [x ~ 10]
        [t ~ 5] => [k ~ 3], [discrete_parameters = k]
    end
end

ModelingToolkit.Model{typeof(Main.var"Main".__M__), Dict{Symbol, Any}}(Main.var"Main".__M__, Dict{Symbol, Any}(:continuous_events => Any["([x ~ 1.5] => [x ~ 5, y ~ 5], ())", "([x ~ 1.5] => [x ~ 5, y ~ 5], ())", "([t ~ 4] => [x ~ 10], ())", "([x ~ 1.5] => [x ~ 5, y ~ 5], ())", "([t ~ 4] => [x ~ 10], ())", "([t ~ 5] => [k ~ 3], [:discrete_parameters => k])"], :variables => Dict{Symbol, Dict{Symbol, Any}}(:y => Dict(:type => Real), :x => Dict(:type => Real)), :kwargs => Dict{Symbol, Dict}(:k => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real), :y => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real), :x => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real)), :independent_variable => :t, :parameters => Dict{Symbol, Dict{Symbol, Any}}(:k => Dict(:type => Real)), :equations => Any["x ~ k * D(x)", "x ~ k * D(x)", "D(y) ~ -k"]), false)

@discrete_events begin block

• Defining discrete events as described here.
• If this block is not defined in the model, no discrete events will be added.
• Discrete parameters and other keyword arguments should be specified in a vector, as seen below.

using ModelingToolkit

@mtkmodel M begin
    @parameters begin
        k(t)
    end
    @variables begin
        x(t)
        y(t)
    end
    @equations begin
        x ~ k * D(x)
        D(y) ~ -k
    end
    @discrete_events begin
        (t == 1.5) => [x ~ Pre(x) + 5, y ~ 5]
        (t == 2.5) => [k ~ Pre(k) * 2], [discrete_parameters = k]
    end
end

ModelingToolkit.Model{typeof(Main.var"Main".__M__), Dict{Symbol, Any}}(Main.var"Main".__M__, Dict{Symbol, Any}(:variables => Dict{Symbol, Dict{Symbol, Any}}(:y => Dict(:type => Real), :x => Dict(:type => Real)), :discrete_events => Any["(t == 1.5 => [x ~ Pre(x) + 5, y ~ 5], ())", "(t == 1.5 => [x ~ Pre(x) + 5, y ~ 5], ())", "(t == 2.5 => [k ~ Pre(k) * 2], [:discrete_parameters => k])"], :kwargs => Dict{Symbol, Dict}(:k => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real), :y => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real), :x => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real)), :independent_variable => :t, :parameters => Dict{Symbol, Dict{Symbol, Any}}(:k => Dict(:type => Real)), :equations => Any["x ~ k * D(x)", "x ~ k * D(x)", "D(y) ~ -k"]), false)

A begin block

• Any other Julia operations can be included with dedicated begin blocks.

Setting the type of system:

By default @mtkmodel returns an System. Different types of system can be defined with the following syntax:

@mtkmodel ModelName::SystemType begin
    ...
end

Connectors

Connectors are special models that can be used to connect different components together. MTK provides 3 distinct connectors:

• DomainConnector: A connector which has only one unknown which is of Flow type, specified by [connect = Flow].
• StreamConnector: A connector which has atleast one stream variable, specified by [connect = Stream]. A StreamConnector must have exactly one flow variable.
• RegularConnector: Connectors that don't fall under above categories.

Defining connectors with @connector

@connector returns ModelingToolkit.Model. It includes a constructor that returns a connector system (System by default), a structure dictionary with metadata, and flag isconnector which is set to true.

A simple connector can be defined with syntax similar to following example:

using ModelingToolkit
using ModelingToolkit: t

@connector Pin begin
    v(t) = 0.0, [description = "Voltage"]
    i(t), [connect = Flow]
end

ModelingToolkit.Model{typeof(Main.__Pin__), Dict{Symbol, Any}}(Main.__Pin__, Dict{Symbol, Any}(:variables => Dict{Symbol, Dict{Symbol, Any}}(:v => Dict(:default => 0.0, :type => Real, :description => "Voltage"), :i => Dict(:type => Real, :connection_type => :Flow)), :kwargs => Dict{Symbol, Dict}(:v => Dict{Symbol, Any}(:value => 0.0, :type => Real), :i => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real)), :independent_variable => :t), true)

Variables (as functions of independent variable) are listed out in the definition. These variables can optionally have initial values and metadata like description, connect and so on. For more details on setting metadata, check out Symbolic Metadata.

Similar to @mtkmodel, @connector accepts begin blocks of @components, @equations, @extend, @parameters, @structural_parameters, @variables. These keywords mean the same as described above for @mtkmodel. For example, the following HydraulicFluid connector is defined with parameters, variables and equations.

@connector HydraulicFluid begin
    @parameters begin
        ρ = 997
        β = 2.09e9
        μ = 0.0010016
        n = 1
        let_gas = 1
        ρ_gas = 0.0073955
        p_gas = -1000
    end
    @variables begin
        dm(t) = 0.0, [connect = Flow]
    end
    @equations begin
        dm ~ 0
    end
end

ModelingToolkit.Model{typeof(Main.__HydraulicFluid__), Dict{Symbol, Any}}(Main.__HydraulicFluid__, Dict{Symbol, Any}(:variables => Dict{Symbol, Dict{Symbol, Any}}(:dm => Dict(:default => 0.0, :type => Real, :connection_type => :Flow)), :kwargs => Dict{Symbol, Dict}(:p_gas => Dict{Symbol, Any}(:value => -1000, :type => Real), :ρ => Dict{Symbol, Any}(:value => 997, :type => Real), :μ => Dict{Symbol, Any}(:value => 0.0010016, :type => Real), :let_gas => Dict{Symbol, Any}(:value => 1, :type => Real), :n => Dict{Symbol, Any}(:value => 1, :type => Real), :ρ_gas => Dict{Symbol, Any}(:value => 0.0073955, :type => Real), :dm => Dict{Symbol, Any}(:value => 0.0, :type => Real), :β => Dict{Symbol, Any}(:value => 2.09e9, :type => Real)), :independent_variable => :t, :parameters => Dict{Symbol, Dict{Symbol, Any}}(:p_gas => Dict(:default => -1000, :type => Real), :ρ => Dict(:default => 997, :type => Real), :μ => Dict(:default => 0.0010016, :type => Real), :let_gas => Dict(:default => 1, :type => Real), :n => Dict(:default => 1, :type => Real), :ρ_gas => Dict(:default => 0.0073955, :type => Real), :β => Dict(:default => 2.09e9, :type => Real)), :equations => Any["dm ~ 0"]), true)

More on Model.structure

structure stores metadata that describes composition of a model. It includes:

• :components: The list of sub-components in the form of [[name, subcomponentname],...].
• :constants: Dictionary of constants mapped to its metadata.
• :defaults: Dictionary of variables and default values specified in the @defaults.
• :extend: The list of extended unknowns, parameters and components, name given to the base system, and name of the base system. When multiple extend statements are present, latter two are returned as lists.
• :structural_parameters: Dictionary of structural parameters mapped to their metadata.
• :parameters: Dictionary of symbolic parameters mapped to their metadata. For parameter arrays, length is added to the metadata as :size.
• :variables: Dictionary of symbolic variables mapped to their metadata. For variable arrays, length is added to the metadata as :size.
• :kwargs: Dictionary of keyword arguments mapped to their metadata.
• :independent_variable: Independent variable, which is added while generating the Model.
• :equations: List of equations (represented as strings).

For example, the structure of ModelC is:

julia> ModelC.structure
Dict{Symbol, Any} with 10 entries:
  :components            => Any[Union{Expr, Symbol}[:model_a, :ModelA], Union{Expr, Symbol}[:model_array_a, :ModelA, :(1:N)], Union{Expr, Symbol}[:model_array_b, :ModelA, :(1:N)]]
  :variables             => Dict{Symbol, Dict{Symbol, Any}}(:v=>Dict(:default=>:v_var, :type=>Real), :v_array=>Dict(:value=>nothing, :type=>Real, :size=>(:N, :M)), :v_for_defaults=>Dict(:type=>Real))
  :icon                  => URI("https://github.com/SciML/SciMLDocs/blob/main/docs/src/assets/logo.png")
  :kwargs                => Dict{Symbol, Dict}(:f=>Dict(:value=>:sin), :p2=>Dict(:value=>NoValue()), :N=>Dict(:value=>2), :M=>Dict(:value=>3), :v=>Dict{Symbol, Any}(:value=>:v_var, :type=>Real), :v_array=>Dict{Symbol, Any}(:value=>nothing, :type=>Real, :size=>(:N, :M)), :v_for_defaults=>Dict{Symbol, Union{Nothing, DataType}}(:value=>nothing, :type=>Real), :p1=>Dict(:value=>1))
  :structural_parameters => Dict{Symbol, Dict}(:f=>Dict(:value=>:sin), :N=>Dict(:value=>2), :M=>Dict(:value=>3))
  :independent_variable  => :t
  :constants             => Dict{Symbol, Dict}(:c=>Dict{Symbol, Any}(:value=>1, :type=>Int64, :description=>"Example constant."))
  :extend                => Any[[:p2, :p1], Symbol("#mtkmodel__anonymous__ModelB"), :ModelB]
  :defaults              => Dict{Symbol, Any}(:v_for_defaults=>2.0)
  :equations             => Any["model_a.k ~ f(v)"]

Different ways to define symbolics arrays:

@mtkmodel supports symbolics arrays in both @parameters and @variables. Using a structural parameters, symbolic arrays of arbitrary lengths can be defined. Refer the following example for different ways to define symbolic arrays.

@mtkmodel ModelWithArrays begin
    @structural_parameters begin
        N = 2
        M = 3
    end
    @parameters begin
        p1[1:4]
        p2[1:N]
        p3[1:N, 1:M] = 10,
        [description = "A multi-dimensional array of arbitrary length with description"]
        (p4[1:N, 1:M] = 10),
        [description = "An alternate syntax for p3 to match the syntax of vanilla parameters macro"]
    end
    @variables begin
        v1(t)[1:2] = 10, [description = "An array of variable `v1`"]
        v2(t)[1:3] = [1, 2, 3]
    end
end

ModelingToolkit.Model{typeof(Main.var"Main".__ModelWithArrays__), Dict{Symbol, Any}}(Main.var"Main".__ModelWithArrays__, Dict{Symbol, Any}(:variables => Dict{Symbol, Dict{Symbol, Any}}(:v2 => Dict(:value => :([1, 2, 3]), :type => Real, :size => (3,)), :v1 => Dict(:value => :v1, :type => Real, :description => "An array of variable `v1`", :size => (2,))), :kwargs => Dict{Symbol, Dict}(:p2 => Dict{Symbol, Any}(:value => nothing, :type => Real, :size => (:N,)), :v1 => Dict{Symbol, Any}(:value => :v1, :type => Real, :description => "An array of variable `v1`", :size => (2,)), :N => Dict(:value => 2), :M => Dict(:value => 3), :p4 => Dict{Symbol, Any}(:value => 10, :type => Real, :description => "An alternate syntax for p3 to match the syntax of vanilla parameters macro", :size => (:N, :M)), :v2 => Dict{Symbol, Any}(:value => :([1, 2, 3]), :type => Real, :size => (3,)), :p1 => Dict{Symbol, Any}(:value => nothing, :type => Real, :size => (4,)), :p3 => Dict{Symbol, Any}(:value => :p3, :type => Real, :description => "A multi-dimensional array of arbitrary length with description", :size => (:N, :M))), :structural_parameters => Dict{Symbol, Dict}(:N => Dict(:value => 2), :M => Dict(:value => 3)), :independent_variable => :t, :parameters => Dict{Symbol, Dict{Symbol, Any}}(:p2 => Dict(:value => nothing, :type => Real, :size => (:N,)), :p4 => Dict(:value => 10, :type => Real, :description => "An alternate syntax for p3 to match the syntax of vanilla parameters macro", :size => (:N, :M)), :p1 => Dict(:value => nothing, :type => Real, :size => (4,)), :p3 => Dict(:value => :p3, :type => Real, :description => "A multi-dimensional array of arbitrary length with description", :size => (:N, :M)))), false)

The size of symbolic array can be accessed via :size key, along with other metadata (refer More on Model.structure) of the symbolic variable.

julia> ModelWithArrays.structure
Dict{Symbol, Any} with 5 entries:
    :variables => Dict{Symbol, Dict{Symbol, Any}}(:v2 => Dict(:value => :([1, 2, 3]), :type => Real, :size => (3,)), :v1 => Dict(:value => :v1, :type => Real, :description => "An array of variable `v1`", :size => (2,)))
    :kwargs => Dict{Symbol, Dict}(:p2 => Dict{Symbol, Any}(:value => nothing, :type => Real, :size => (:N,)), :v1 => Dict{Symbol, Any}(:value => :v1, :type => Real, :description => "An array of variable `v1`", :size => (2,)), :N => Dict(:value => 2), :M => Dict(:value => 3), :p4 => Dict{Symbol, Any}(:value => 10, :type => Real, :description => "An alternate syntax for p3 to match the syntax of vanilla parameters macro", :size => (:N, :M)), :v2 => Dict{Symbol, Any}(:value => :([1, 2, 3]), :type => Real, :size => (3,)), :p1 => Dict{Symbol, Any}(:value => nothing, :type => Real, :size => (4,)), :p3 => Dict{Symbol, Any}(:value => :p3, :type => Real, :description => "A multi-dimensional array of arbitrary length with description", :size => (:N, :M)))
    :structural_parameters => Dict{Symbol, Dict}(:N => Dict(:value => 2), :M => Dict(:value => 3))
    :independent_variable => :t
    :parameters => Dict{Symbol, Dict{Symbol, Any}}(:p2 => Dict(:value => nothing, :type => Real, :size => (:N,)), :p4 => Dict(:value => 10, :type => Real, :description => "An alternate syntax for p3 to match the syntax of vanilla parameters macro", :size => (:N, :M)), :p1 => Dict(:value => nothing, :type => Real, :size => (4,)), :p3 => Dict(:value => :p3, :type => Real, :description => "A multi-dimensional array of arbitrary length with description", :size => (:N, :M)))), false)

Using conditional statements

Conditional elements of the system

Both @mtkmodel and @connector support conditionally defining parameters, variables, equations, and components.

The if-elseif-else statements can be used inside @equations, @parameters, @variables, @components.

using ModelingToolkit
using ModelingToolkit: t

@mtkmodel C begin end

@mtkmodel BranchInsideTheBlock begin
    @structural_parameters begin
        flag = true
    end
    @parameters begin
        if flag
            a1
        else
            a2
        end
    end
    @components begin
        if flag
            sys1 = C()
        else
            sys2 = C()
        end
    end
end

ModelingToolkit.Model{typeof(Main.var"Main".__BranchInsideTheBlock__), Dict{Symbol, Any}}(Main.var"Main".__BranchInsideTheBlock__, Dict{Symbol, Any}(:components => Any[(:if, :flag, Vector{Union{Expr, Symbol}}[[:sys1, :C]], Vector{Union{Expr, Symbol}}[[:sys2, :C]])], :kwargs => Dict{Symbol, Dict}(:flag => Dict{Symbol, Bool}(:value => 1)), :structural_parameters => Dict{Symbol, Dict}(:flag => Dict{Symbol, Bool}(:value => 1)), :independent_variable => t, :parameters => Dict{Symbol, Dict{Symbol, Any}}(:a2 => Dict(:type => AbstractArray{Real}, :condition => (:if, :flag, Dict{Symbol, Any}(:kwargs => Dict{Any, Any}(:a1 => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real)), :parameters => Any[Dict{Symbol, Dict{Symbol, Any}}(:a1 => Dict(:type => AbstractArray{Real}))]), Dict{Symbol, Any}(:variables => Any[Dict{Symbol, Dict{Symbol, Any}}()], :kwargs => Dict{Any, Any}(:a2 => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real)), :constants => Any[Dict{Symbol, Dict{Symbol, Any}}()], :parameters => Any[Dict{Symbol, Dict{Symbol, Any}}(:a2 => Dict(:type => AbstractArray{Real}))]))), :a1 => Dict(:type => AbstractArray{Real}, :condition => (:if, :flag, Dict{Symbol, Any}(:kwargs => Dict{Any, Any}(:a1 => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real)), :parameters => Any[Dict{Symbol, Dict{Symbol, Any}}(:a1 => Dict(:type => AbstractArray{Real}))]), Dict{Symbol, Any}(:variables => Any[Dict{Symbol, Dict{Symbol, Any}}()], :kwargs => Dict{Any, Any}(:a2 => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real)), :constants => Any[Dict{Symbol, Dict{Symbol, Any}}()], :parameters => Any[Dict{Symbol, Dict{Symbol, Any}}(:a2 => Dict(:type => AbstractArray{Real}))]))))), false)

Alternatively, the @equations, @parameters, @variables, @components can be used inside the if-elseif-else statements.

@mtkmodel BranchOutsideTheBlock begin
    @structural_parameters begin
        flag = true
    end
    if flag
        @parameters begin
            a1
        end
        @components begin
            sys1 = C()
        end
        @equations begin
            a1 ~ 0
        end
    else
        @parameters begin
            a2
        end
        @equations begin
            a2 ~ 0
        end
    end
    @defaults begin
        a1 => 10
    end
end

ModelingToolkit.Model{typeof(Main.var"Main".__BranchOutsideTheBlock__), Dict{Symbol, Any}}(Main.var"Main".__BranchOutsideTheBlock__, Dict{Symbol, Any}(:components => Any[(:if, :flag, Vector{Union{Expr, Symbol}}[[:sys1, :C]], Any[])], :kwargs => Dict{Symbol, Dict}(:flag => Dict{Symbol, Bool}(:value => 1)), :structural_parameters => Dict{Symbol, Dict}(:flag => Dict{Symbol, Bool}(:value => 1)), :independent_variable => t, :parameters => Dict{Symbol, Dict{Symbol, Any}}(:a2 => Dict(:type => AbstractArray{Real}, :condition => (:if, :flag, Dict{Symbol, Any}(:kwargs => Dict{Any, Any}(:a1 => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real)), :parameters => Any[Dict{Symbol, Dict{Symbol, Any}}(:a1 => Dict(:type => AbstractArray{Real}))]), Dict{Symbol, Any}(:variables => Any[Dict{Symbol, Dict{Symbol, Any}}()], :kwargs => Dict{Any, Any}(:a2 => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real)), :constants => Any[Dict{Symbol, Dict{Symbol, Any}}()], :parameters => Any[Dict{Symbol, Dict{Symbol, Any}}(:a2 => Dict(:type => AbstractArray{Real}))]))), :a1 => Dict(:type => AbstractArray{Real}, :condition => (:if, :flag, Dict{Symbol, Any}(:kwargs => Dict{Any, Any}(:a1 => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real)), :parameters => Any[Dict{Symbol, Dict{Symbol, Any}}(:a1 => Dict(:type => AbstractArray{Real}))]), Dict{Symbol, Any}(:variables => Any[Dict{Symbol, Dict{Symbol, Any}}()], :kwargs => Dict{Any, Any}(:a2 => Dict{Symbol, Union{Nothing, DataType}}(:value => nothing, :type => Real)), :constants => Any[Dict{Symbol, Dict{Symbol, Any}}()], :parameters => Any[Dict{Symbol, Dict{Symbol, Any}}(:a2 => Dict(:type => AbstractArray{Real}))])))), :defaults => Dict{Symbol, Any}(:a1 => 10), :equations => Any[(:if, :flag, ["a1 ~ 0"], ["a2 ~ 0"])]), false)

The conditional parts are reflected in the structure. For BranchOutsideTheBlock, the metadata is:

julia> BranchOutsideTheBlock.structure
Dict{Symbol, Any} with 7 entries:
  :components            => Any[(:if, :flag, Vector{Union{Expr, Symbol}}[[:sys1, :C]], Any[])]
  :kwargs                => Dict{Symbol, Dict}(:flag=>Dict{Symbol, Bool}(:value=>1))
  :structural_parameters => Dict{Symbol, Dict}(:flag=>Dict{Symbol, Bool}(:value=>1))
  :independent_variable  => t
  :parameters            => Dict{Symbol, Dict{Symbol, Any}}(:a2 => Dict(:type=>AbstractArray{Real}, :condition=>(:if, :flag, Dict{Symbol, Any}(:kwargs=>Dict{Any, Any}(:a1=>Dict{Symbol, Union{Nothing, DataType}}(:value=>nothing, :type=>Real)), :parameters=>Any[Dict{Symbol, Dict{Symbol, Any}}(:a1=>Dict(:type=>AbstractArray{Real}))]), Dict{Symbol, Any}(:variables=>Any[Dict{Symbol, Dict{Symbol, Any}}()], :kwargs=>Dict{Any, Any}(:a2=>Dict{Symbol, Union{Nothing, DataType}}(:value=>nothing, :type=>Real)), :parameters=>Any[Dict{Symbol, Dict{Symbol, Any}}(:a2=>Dict(:type=>AbstractArray{Real}))]))), :a1 => Dict(:type=>AbstractArray{Real}, :condition=>(:if, :flag, Dict{Symbol, Any}(:kwargs=>Dict{Any, Any}(:a1=>Dict{Symbol, Union{Nothing, DataType}}(:value=>nothing, :type=>Real)), :parameters=>Any[Dict{Symbol, Dict{Symbol, Any}}(:a1=>Dict(:type=>AbstractArray{Real}))]), Dict{Symbol, Any}(:variables=>Any[Dict{Symbol, Dict{Symbol, Any}}()], :kwargs=>Dict{Any, Any}(:a2=>Dict{Symbol, Union{Nothing, DataType}}(:value=>nothing, :type=>Real)), :parameters=>Any[Dict{Symbol, Dict{Symbol, Any}}(:a2=>Dict(:type=>AbstractArray{Real}))]))))
  :defaults              => Dict{Symbol, Any}(:a1=>10)
  :equations             => Any[(:if, :flag, ["a1 ~ 0"], ["a2 ~ 0"])]

Conditional entries are entered in the format of (branch, condition, [case when it is true], [case when it is false]); where branch is either :if or :elseif.<br> The [case when it is false] is either an empty vector or nothing when only if branch is present; it is a vector or dictionary whenever else branch is present; it is a conditional tuple whenever elseif branches are present.

For the conditional components and equations these condition tuples are added directly, while for parameters and variables these are added as :condition metadata.

Conditional initial guess of symbolic variables

Using ternary operator or if-elseif-else statement, conditional initial guesses can be assigned to parameters and variables.

@mtkmodel DefaultValues begin
    @structural_parameters begin
        flag = true
    end
    @parameters begin
        p = flag ? 1 : 2
    end
end

ModelingToolkit.Model{typeof(Main.var"Main".__DefaultValues__), Dict{Symbol, Any}}(Main.var"Main".__DefaultValues__, Dict{Symbol, Any}(:kwargs => Dict{Symbol, Dict}(:p => Dict{Symbol, Any}(:value => :(if flag
      1
  else
      2
  end), :type => Real), :flag => Dict{Symbol, Bool}(:value => 1)), :structural_parameters => Dict{Symbol, Dict}(:flag => Dict{Symbol, Bool}(:value => 1)), :independent_variable => t, :parameters => Dict{Symbol, Dict{Symbol, Any}}(:p => Dict(:default => :(if flag
      1
  else
      2
  end), :type => Real))), false)

Build structurally simplified models:

@mtkcompile builds an instance of a component and returns a structurally simplied system.

@mtkcompile sys = CustomModel()

This is equivalent to:

@named model = CustomModel()
sys = mtkcompile(model)

Pass keyword arguments to mtkcompile using the following syntax:

@mtkcompile sys=CustomModel() fully_determined=false

This is equivalent to:

@named model = CustomModel()
sys = mtkcompile(model; fully_determined = false)