Control Input for NeuralODE

[MortezaBabazadehShareh]

How can we define a control input for a Neural ODE? The control input is an array with a specific value for each time step.

[ChrisRackauckas]

Just use DataInterpolations to make the interpolation.

[MortezaBabazadehShareh]

After this Interpolation:

Control=LinearInterpolation(u,tsteps);

How should I use the Control as an external control signal in the following code?

data_dim=size(ode_data[:, 1])[1]
dudt2 = Lux.Chain(Lux.Dense(data_dim, 64, relu),
    Lux.Dense(64, 32, relu),
    Lux.Dense(32, data_dim),
    )

rng = Random.default_rng()
p, st = Lux.setup(rng, dudt2)
prob_neuralode = NeuralODE(dudt2, tspan, Tsit5(), saveat = tsteps)

The Control is the daily vaccination rate, and the primary variable in the ode_data is the Infection number.

[Spinachboul]

@ChrisRackauckas and @MortezaBabazadehShareh

![Just a concept code, could be taken into consideration]

In the above code snippet, we can modify it slightly to externally include the control input as an added input while building the neural networks layers using Flux

Here is the code snippet:

# Include the required packages

# Assuming ```LinearInterpolation(x, tsteps)``` is defined to get Control(t)

# Define the Neural ODE model
data_dim = size(ode_data[:, 1])[1]
dudt2 = Flux.Chain(
    Flux.Dense(data_dim + 1, 64, relu),  # +1 for the control input
    Flux.Dense(64, 32, relu),
    Flux.Dense(32, data_dim)
)

# Initialize the parameters rng, p and st

# Function to calculate ODE with control input
function dudt_with_control(u, p, t)
    control_input = Control(t)  # Assuming Control is a function of time
    u_with_control = vcat(u, control_input)
    Flux.mlp(p, u_with_control)
end

# Then the further steps include training and loss calculations

Here, dudt_with_control is a modified function that takes the state u, parameters p, and time t, and appends the control input at each time step. The control input is assumed to be obtained from the function Control(t). The rest of the code is adjusted accordingly to incorporate this modified model into the Neural ODE and for training.