# Deploying a Lotka-Volterra FMU model

In this example we will demonstrate how to deploy a Lotka-Volterra model as a FMU using `FMUGeneration.jl`

. We start by loading `FMUGeneration`

and `OrdinaryDiffEq`

into our environment.

```
using FMUGeneration
using OrdinaryDiffEq
```

For the tutorial, we chose a Lotka Volterra system with controls. This system is a pair of non-linear differential equations used to describe the dynamics of a biological system. The system has a set of parameters `α`

, `β`

, `γ`

, `δ`

and `u₁`

, `u₂`

are time-dependent controls.

\[\frac{dx₁}{dt} = \alpha x₁ - \beta x₁x₂ + u₁ \]

\[\frac{dx₂}{dt} = \delta x₁x₂ - \gamma x₂ - u₂\]

FMUGeneration.jl first creates a package for the FMU containing the necessary functions, models, and variables, then builds a sysimage.

We define the above system as an expression to be packaged into an FMU as follows:

```
lv_expr = :(function (dx, x, u, p, t)
x₁, x₂ = x
u₁, u₂ = u
α, β, γ, δ = p
dx₁ = α * x₁ - β * x₁ * x₂ + u₁
dx₂ = δ * x₁ * x₂ - γ * x₂ - u₂
dx = [dx₁, dx₂]
end);
```

```
:(function (dx, x, u, p, t)
#= lv.md:24 =#
#= lv.md:25 =#
(x₁, x₂) = x
#= lv.md:26 =#
(u₁, u₂) = u
#= lv.md:27 =#
(α, β, γ, δ) = p
#= lv.md:28 =#
dx₁ = (α * x₁ - β * x₁ * x₂) + u₁
#= lv.md:29 =#
dx₂ = (δ * x₁ * x₂ - γ * x₂) - u₂
#= lv.md:30 =#
dx = [dx₁, dx₂]
end)
```

Once we have defined our system and continuous model, we need to define some defaults for the system. These include initial states, initial inputs, default parameters, and the timespan.

```
initial_states = [1.0, 1.0]
initial_inputs = [0.01, 0.01]
default_parameters = [2.0, 1.875, 2.0, 1.875]
tspan = (0.0, 10.0)
param_names = ["α", "β", "γ", "δ"]
input_names = ["u_1" , "u_2"]
state_names = ["x_1" , "x_2"]
```

```
2-element Vector{String}:
"x_1"
"x_2"
```

We then instantiate a `JuliaFMU`

object which comines the meradata, dependencies and dynamics which make up the FMU. This implicitly generates the metadata.

```
fmu = JuliaFMU(
# REQUIRED ARGUMENTS
# We specify the FMU name
"lotka-volterra",
# We specify the FMI version
FMI_V3, # or v2,
# We specify the FMU operating types supported
[FMI_MODELEXCHANGE, FMI_COSIMULATION];
# OPTIONAL ARGUMENTS
# We optionally specify the default time-space of the FMU operation
default_tspan = tspan,
# We optionally specify the recommended step size
# default_stepsize = 1e-3,
# We optionally specify the recommended solver tolerance
# default_tolerance = 1e-6,
# Metadata: inputs, parameters and states respectively
inputs = [
(name=input_names[i], start=initial_inputs[i]) for i in 1:length(input_names)
],
parameters = [
(name=param_names[i], start=default_parameters[i]) for i in 1:length(param_names)
],
states = [
(name=state_names[i], start=initial_states[i]) for i in 1:length(state_names)
],
# We define the dependencies required for the FMU. Here, we need OrdinaryDiffEq for the solver used to run the FMU in CS mode.
dependencies = @deps([OrdinaryDiffEq]),
# We define the ODE function expression with the signature `(dx, u, p, t) -> begin ... end` where the function is expected to be inplace. Here, it is the `double_pendulum_expr` defined earlier. This is an essential kwarg for all ME FMUs.
ode_function = lv_expr,
# We optionally define function to compute the outputs with the signature `(x, u, p, t) -> outs`.
# observables_function = observable_expr,
# We specify which solver to use for cosimulation. We default to `OrdinaryDiffEq.AutoTsit5(OrdinaryDiffEq.FBDF())` if not provided.
cosimulator_solver = :(OrdinaryDiffEq.AutoTsit5(OrdinaryDiffEq.FBDF())),
# If we had inputs, we would also had to specify it like below:
# inputs = [
# (name="input_1", start=1.0),
# ...
# ],
# If we had to initialize out states in a specific manner, we could also that like below:
# state_initializer = :((x, u, p, t) -> initialize_x)
# We could also optionally provide integrator options:
# cosimulator_integrator_options=(abstol=1e-6, reltol=1e-6),
# We could also optionally provide objects from user space needed for the FMU dynamics to operate
# objects=@objects([test_obj]),
# We optionally define the number of threads to start the FMU with to capitalize on multi-threaded acceleration of matmul operations. This is only relevant if your computation is heavy on matrix operations.
# n_octavian_threads = 4
)
```

```
Functional Mockup Unit: lotka-volterra
FMI Specification:
Version: v3
Types: ["modelExchange", "coSimulation"]
Default Experiment Setup:
Time Span: (0.0, 10.0)
Step Size: nothing
Tolerance: nothing
Paths:
Temp: /home/github_actions/actions-runner-1/home/.julia/scratchspaces/ca28fe3e-7809-4c0f-9d3e-a21c6e6f3e9d/JSDeploymentjl/wFHgQT
Julia Package: /home/github_actions/actions-runner-1/home/.julia/scratchspaces/ca28fe3e-7809-4c0f-9d3e-a21c6e6f3e9d/JSDeploymentjl/wFHgQT/FMIBinary_wFHgQT.jl
JuliaFMU: /home/github_actions/actions-runner-1/home/.julia/scratchspaces/ca28fe3e-7809-4c0f-9d3e-a21c6e6f3e9d/JSDeploymentjl/wFHgQT/lotka-volterra.fmu
Metadata XML: /home/github_actions/actions-runner-1/home/.julia/scratchspaces/ca28fe3e-7809-4c0f-9d3e-a21c6e6f3e9d/JSDeploymentjl/wFHgQT/modelDescription.xml
```