Neural network tutorial

Note

This surrogate requires the 'SurrogatesFlux' module which can be added by inputting "]add SurrogatesFlux" from the Julia command line.

It's possible to define a neural network as a surrogate, using Flux. This is useful because we can call optimization methods on it.

First of all we will define the Schaffer function we are going to build surrogate for.

using Plots
default(c=:matter, legend=false, xlabel="x", ylabel="y") # hide
using Surrogates
using Flux
using SurrogatesFlux

function schaffer(x)
x1=x[1]
x2=x[2]
fact1 = x1 ^2;
fact2 = x2 ^2;
y = fact1 + fact2;
end

Sampling

Let's define our bounds, this time we are working in two dimensions. In particular we want our first dimension x to have bounds 0, 8, and 0, 8 for the second dimension. We are taking 60 samples of the space using Sobol Sequences. We then evaluate our function on all of the sampling points.

n_samples = 60
lower_bound = [0.0, 0.0]
upper_bound = [8.0, 8.0]

xys = sample(n_samples, lower_bound, upper_bound, SobolSample())
zs = schaffer.(xys);
x, y = 0:8, 0:8 # hide
p1 = surface(x, y, (x1,x2) -> schaffer((x1,x2))) # hide
xs = [xy[1] for xy in xys] # hide
ys = [xy[2] for xy in xys] # hide
scatter!(xs, ys, zs) # hide
p2 = contour(x, y, (x1,x2) -> schaffer((x1,x2))) # hide
scatter!(xs, ys) # hide
plot(p1, p2, title="True function") # hide

Building a surrogate

You can specify your own model, optimization function, loss functions and epochs. As always, getting the model right is hardest thing.

model1 = Chain(
Dense(2, 5, σ),
Dense(5,2,σ),
Dense(2, 1)
)
neural = NeuralSurrogate(xys, zs, lower_bound, upper_bound, model = model1, n_echos = 10)

Optimization

We can now call an optimization function on the neural network:

surrogate_optimize(schaffer, SRBF(), lower_bound, upper_bound, neural, SobolSample(), maxiters=20, num_new_samples=10)