# Specify names of states and parameters in ODEProblem?

**URL:** <https://discourse.julialang.org/t/specify-names-of-states-and-parameters-in-odeproblem/115145>\
**Category:** Modelling & Simulations\
**Created:** [June 4, 2024, 12:27am UTC](https://discourse.julialang.org/t/specify-names-of-states-and-parameters-in-odeproblem/115145 "2024-06-04T00:27:55Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![sdwfrost](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sdwfrost/32/2831_2.png) [@sdwfrost](https://discourse.julialang.org/u/sdwfrost)\
**Post date:** [June 4, 2024, 12:27am UTC](https://discourse.julialang.org/t/specify-names-of-states-and-parameters-in-odeproblem/115145/1 "2024-06-04T00:27:55Z")

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Here’s a simple problem I have where I couldn’t find any documentation; I’d like to specify the parameter names of the states and parameters to SciML’s `ODEFunction` e.g. using `Dict(:u => [:S, :I, :R], :p => [:β, :c, :γ])`. Here’s a complete example that doesn’t specify the names. I know that this is done automatically using ModelingToolkit, but I want to use vanilla Julia. Any suggestions?

```Julia
function sir_ode!(du,u,p,t)
    (S,I,R) = u
    (β,c,γ) = p
    N = S+I+R
    @inbounds begin
        du[1] = -β*c*I/N*S
        du[2] = β*c*I/N*S - γ*I
        du[3] = γ*I
    end
    nothing
end
prob_ode = ODEProblem(sir_ode!, u0, tspan, p)
sol_ode = solve(prob_ode, Tsit5(), dt = δt)

```

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [June 4, 2024, 4:05am UTC](https://discourse.julialang.org/t/specify-names-of-states-and-parameters-in-odeproblem/115145/2 "2024-06-04T04:05:54Z")

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This is all defined in [Home · SymbolicIndexingInterface.jl](https://docs.sciml.ai/SymbolicIndexingInterface/stable/)

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**Author:** ![sdwfrost](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sdwfrost/32/2831_2.png) [@sdwfrost](https://discourse.julialang.org/u/sdwfrost)\
**Post date:** [June 4, 2024, 4:25am UTC](https://discourse.julialang.org/t/specify-names-of-states-and-parameters-in-odeproblem/115145/3 "2024-06-04T04:25:20Z")

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Thanks Chris! Just what I was looking for…

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<div class="post-metadata">

**Author:** ![sdwfrost](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sdwfrost/32/2831_2.png) [@sdwfrost](https://discourse.julialang.org/u/sdwfrost)\
**Post date:** [June 4, 2024, 2:15pm UTC](https://discourse.julialang.org/t/specify-names-of-states-and-parameters-in-odeproblem/115145/4 "2024-06-04T14:15:05Z")

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One more thing; while this gives me a way to index the solution (e.g. `sol[:S]`), the names don’t show up automatically when I plot the solution (U just get `u[1]` etc.). Is there a way to show the defined symbols when plotting?

```julia
using OrdinaryDiffEq
using SymbolicIndexingInterface
using ModelingToolkit
using Plots

function sir_ode!(du,u,p,t)
    (S,I,R) = u
    (β,c,γ) = p
    N = S+I+R
    @inbounds begin
        du[1] = -β*c*I/N*S
        du[2] = β*c*I/N*S - γ*I
        du[3] = γ*I
    end
    nothing
end
sys = SymbolCache([:S,:I,:R],[:β,:c,:γ],:t)
fun = ODEFunction(sir_ode!; sys=sys)
prob = ODEProblem(fun, u0, tspan, p)
sol = solve(prob, Tsit5(), dt = δt)
plot(sol)

```

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [June 4, 2024, 5:36pm UTC](https://discourse.julialang.org/t/specify-names-of-states-and-parameters-in-odeproblem/115145/5 "2024-06-04T17:36:08Z")

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The plots should already use that? If not, then it needs some work in the plot recipe. It just asks the sys for the names to generate the labels. @cryptic.ax is SymbolCache missing a dispatch on nameof or something?

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<div class="post-metadata">

**Author:** ![sdwfrost](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sdwfrost/32/2831_2.png) [@sdwfrost](https://discourse.julialang.org/u/sdwfrost)\
**Post date:** [June 4, 2024, 7:19pm UTC](https://discourse.julialang.org/t/specify-names-of-states-and-parameters-in-odeproblem/115145/6 "2024-06-04T19:19:02Z")

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The plot recipe definitely doesn’t use that; here’s the full code for debugging purposes:

```julia
using OrdinaryDiffEq
using SymbolicIndexingInterface
using ModelingToolkit
using Plots

function sir_ode!(du,u,p,t)
    (S,I,R) = u
    (β,c,γ) = p
    N = S+I+R
    @inbounds begin
        du[1] = -β*c*I/N*S
        du[2] = β*c*I/N*S - γ*I
        du[3] = γ*I
    end
    nothing
end
sys = SymbolCache([:S,:I,:R],[:β,:c,:γ],:t)
fun = ODEFunction(sir_ode!; sys=sys)

δt = 0.1
tmax = 40.0
tspan = (0.0,tmax)
u0 = [990.0,10.0,0.0] # S,I,R
p = [0.05,10.0,0.25] # β,c,γ
prob = ODEProblem(fun, u0, tspan, p)
sol = solve(prob, Tsit5(), dt = δt)
plot(sol)

```

The symbols are also lost during modelingtoolkitize too:

```julia
sys_mtk = modelingtoolkitize(prob)

```

gives:

```julia
julia> sys_mtk.eqs
Equation[Differential(t)(x₁(t)) ~ (-α₁*α₂*x₁(t)*x₂(t)) / (x₁(t) + x₂(t) + x₃(t)), Differential(t)(x₂(t)) ~ (α₁*α₂*x₁(t)*x₂(t)) / (x₁(t) + x₂(t) + x₃(t)) - α₃*x₂(t), Differential(t)(x₃(t)) ~ α₃*x₂(t)][1:3]

Model ##MTKizedODE#710 with 3 equations
States (3):
  x₁(t) [defaults to 990.0]
  x₂(t) [defaults to 10.0]
⋮
Parameters (3):
  α₁ [defaults to 0.05]
  α₂ [defaults to 10.0]
⋮

```

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<div class="post-metadata">

**Author:** ![cryptic.ax](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cryptic.ax/32/220540_2.png) [@cryptic.ax](https://discourse.julialang.org/u/cryptic.ax)\
**Post date:** [June 5, 2024, 6:24am UTC](https://discourse.julialang.org/t/specify-names-of-states-and-parameters-in-odeproblem/115145/7 "2024-06-05T06:24:46Z")

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I’ll look into this, the plot recipes should respect the symbol names.

> The symbols are also lost during modelingtoolkitize too:

That’s not implemented yet, but it is possible.