Package 'tfNeuralODE'

Backward pass of the Neural ODE

Description

Backward pass of the Neural ODE

Usage

backward(model, tsteps, outputs, output_gradients = NULL)

Arguments

model	A keras neural network that defines the Neural ODE.
tsteps	A vector of each time step upon which the Neural ODE is solved to get to the final solution.
outputs	The tensor outputs of the forward pass of the Neural ODE.
output_gradients	The tensor gradients of the loss function.

Value

The model input at the last time step.

The gradient of loss with respect to the inputs for use with the Adjoint Method.

The gradients of loss the neural ODE.

Examples

reticulate::py_module_available("tensorflow")

# example code
# single training example
OdeModel(keras$Model) %py_class% {
 initialize <- function() {
   super$initialize()
   self$block_1 <- layer_dense(units = 50, activation = 'tanh')
   self$block_2 <- layer_dense(units = 2, activation = 'linear')
 }

 call <- function(inputs) {
   x<- inputs ^ 3
   x <- self$block_1(x)
   self$block_2(x)
 }
}
tsteps <- seq(0, 2.5, by = 2.5/10)
true_y0 = t(c(2., 0.))
model<- OdeModel()
optimizer = tf$keras$optimizers$legacy$Adam(learning_rate = 1e-3)
# single training iteration
pred = forward(model, true_y0, tsteps)
with(tf$GradientTape() %as% tape, {
  tape$watch(pred)
  loss = tf$reduce_mean(tf$abs(pred - inp[[2]]))
})
dLoss = tape$gradient(loss, pred)
list_w = backward(model, tsteps[1:batch_time], pred, output_gradients = dLoss)
optimizer$apply_gradients(zip_lists(list_w[[3]], model$trainable_variables))

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Forward pass of the Neural ODE network

Description

Forward pass of the Neural ODE network

Usage

forward(model, inputs, tsteps, return_states = FALSE)

Arguments

model	A keras neural network that defines the Neural ODE.
inputs	Matrix or vector inputs to the neural network.
tsteps	A vector of each time step upon which the Neural ODE is solved to get to the final solution.
return_states	A boolean which dictates whether the intermediary states between the input and the final solution are returned.

Value

solution of the forward pass of Neural ODE

Examples

reticulate::py_module_available("tensorflow")

# example code

library(tensorflow)
library(keras)

OdeModel(keras$Model) %py_class% {
 initialize <- function() {
   super$initialize()
   self$block_1 <- layer_dense(units = 50, activation = 'tanh')
   self$block_2 <- layer_dense(units = 2, activation = 'linear')
 }

 call <- function(inputs) {
   x<- inputs ^ 3
   x <- self$block_1(x)
   self$block_2(x)
 }
}
tsteps <- seq(0, 2.5, by = 2.5/10)
true_y0 = t(c(2., 0.))
model<- OdeModel()
forward(model, true_y0, tsteps)

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Runge Kutta solver for ordinary differential equations

Description

Runge Kutta solver for ordinary differential equations

Usage

rk4_step(func, dt, state)

Arguments

func	The function to be numerically integrated.
dt	Time step.
state	A list describing the state of the function, with the first element being 1, and the second being a tensor that represents state

Value

A list containing a new time and the numerical integration of of the function across the time step to the new time.

Examples

reticulate::py_module_available("tensorflow")
# example code
library(tensorflow)
ode_fun<- function(u){
  r = u ^ 3
  true_A = rbind(c(-0.1, 2.0), c(-2.0, -0.1))
  du <- r %*% (true_A)
  return(as.matrix(du))
}
y<- tensorflow::tf$cast(t(as.matrix(c(2, 0))), dtype = tf$float32)
x<- rk4_step(ode_fun,  dt = 0.25,
            state = list(1.0, y))
x

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