I have recently started using Flux to construct a physics informed neural network. To do this, I start with a model
u = Chain(Dense(1, 10), Dense(10,15), Dense(15,1))
Then I construct a function to impose the differential condition y’(t) - y(t) = 0
y = sum(u(t))
dy = gradient(() -> u(t), params(t))
f = dy[t] - y
with cost function
cost(t) = abs(f(t))^2
I would like to minimize this cost with respect to the parameters of u but when I call
grad = gradient(() -> cost(t), params(u))
I get a long stacktrace starting with “ERROR: Can’t differentiate foreigncall expression”. The full stacktrace is in this gist.
I am having troubles figuring out what is causing the error. I want to be able to train a network u(x) to respect a condition u’(x) - u(x) = 0 but don’t know how to specify this with Flux. If anyone has any suggestions I would greatly appreciate it.