## Getting the index for a symbol

Since ordering of symbols is not guaranteed after symbolic transformations, one should normally refer to values by their name. For example, sol[lorenz.x] from the solution. But what if you need to get the index? The following helper function will do the trick:

indexof(sym,syms) = findfirst(isequal(sym),syms)
indexof(σ,parameters(sys))

## Transforming value maps to arrays

ModelingToolkit.jl allows (and recommends) input maps like [x => 2.0, y => 3.0] because symbol ordering is not guaranteed. However, what if you want to get the lowered array? You can use the internal function varmap_to_vars. For example:

pnew = varmap_to_vars([β=>3.0, c=>10.0, γ=>2.0],parameters(sys))

## How do I handle if statements in my symbolic forms?

For statements that are in the if then else form, use IfElse.ifelse from the IfElse.jl package to represent the code in a functional form. For handling direct if statements, you can use equivalent boolean mathematical expressions. For example if x > 0 ... can be implemented as just (x > 0) *, where if x <= 0 then the boolean will evaluate to 0 and thus the term will be excluded from the model.

## ERROR: TypeError: non-boolean (Num) used in boolean context?

If you see the error:

ERROR: TypeError: non-boolean (Num) used in boolean context

then it's likely you are trying to trace through a function which cannot be directly represented in Julia symbols. The techniques to handle this problem, such as @register_symbolic, are described in detail in the Symbolics.jl documentation.

## Using ModelingToolkit with Optimization / Automatic Differentiation

If you are using ModelingToolkit inside of a loss function and are having issues with mixing MTK with automatic differentiation, getting performance, etc... don't! Instead, use MTK outside of the loss function to generate the code, and then use the generated code inside of the loss function.

For example, let's say you were building ODEProblems in the loss function like:

function loss(p)
prob = ODEProblem(sys, [], [p1 => p[1], p2 => p[2]])
sol = solve(prob, Tsit5())
sum(abs2,sol)
end

Since ODEProblem on a MTK sys will have to generate code, this will be slower than caching the generated code, and will required automatic differentiation to go through the code generation process itself. All of this is unnecessary. Instead, generate the problem once outside of the loss function, and remake the prob inside of the loss function:

prob = ODEProblem(sys, [], [p1 => p[1], p2 => p[2]])
function loss(p)
remake(prob,p = ...)
sol = solve(prob, Tsit5())
sum(abs2,sol)
end

Now, one has to be careful with remake to ensure that the parameters are in the right order. One can use the previously mentioned indexing functionality to generate index maps for reordering p like:

p = @parameters x y z
idxs = ModelingToolkit.varmap_to_vars([p[1] => 1, p[2] => 2, p[3] => 3], p)
p[idxs]

Using this, the fixed index map can be used in the loss function. This would look like:

prob = ODEProblem(sys, [], [p1 => p[1], p2 => p[2]])
idxs = Int.(ModelingToolkit.varmap_to_vars([p1 => 1, p2 => 2], p))
function loss(p)
remake(prob,p = p[idxs])
sol = solve(prob, Tsit5())
sum(abs2,sol)
end