I tried using this example found here: https://github.com/SciML/NeuralPDE.jl but I get the error “ERROR: LoadError: LoadError: UndefVarError: AbstractADType not defined” during the precompilation of the GalacticOptim package.

Here is the code:

```
using NeuralPDE, Flux, ModelingToolkit, Optim, DiffEqFlux
using GalacticOptim
using Base
#GalacticOptim
# 3D PDE
@parameters x y t θ
@variables u(..)
@derivatives Dxx''~x
@derivatives Dyy''~y
@derivatives Dt'~t
# 3D PDE
eq = Dt(u(x,y,t,θ)) ~ Dxx(u(x,y,t,θ)) + Dyy(u(x,y,t,θ))
# Initial and boundary conditions
bcs = [u(x,y,0,θ) ~ exp(x+y)*cos(x+y) ,
u(0,y,t,θ) ~ exp(y)*cos(y+4t),
u(2,y,t,θ) ~ exp(2+y)*cos(2+y+4t) ,
u(x,0,t,θ) ~ exp(x)*cos(x+4t),
u(x,2,t,θ) ~ exp(x+2)*cos(x+2+4t)]
# Space and time domains
domains = [x ∈ IntervalDomain(0.0,2.0),
y ∈ IntervalDomain(0.0,2.0),
t ∈ IntervalDomain(0.0,2.0)]
# Discretization
dx = 0.25; dy= 0.25; dt = 0.25
# Neural network
chain = FastChain(FastDense(3,16,Flux.σ),FastDense(16,16,Flux.σ),FastDense(16,1))
discretization = NeuralPDE.PhysicsInformedNN([dx,dy,dt],
chain,
strategy = NeuralPDE.StochasticTraining(include_frac=0.9))
pde_system = PDESystem(eq,bcs,domains,[x,y,t],[u])
prob = NeuralPDE.discretize(pde_system,discretization)
res = GalacticOptim.solve(prob, ADAM(0.1), progress = false; cb = cb, maxiters=3000)
phi = discretization.phi
ts,xs = [domain.domain.lower:dx:domain.domain.upper for domain in domains]
analytic_sol_func(t,x) = [exp(-t)*sin(pi*x), exp(-t)*cos(pi*x), (1+pi^2)*exp(-t)]
u_real = [[analytic_sol_func(t,x)[i] for t in ts for x in xs] for i in 1:3]
u_predict = [[phi([t,x],res.minimizer)[i] for t in ts for x in xs] for i in 1:3]
diff_u = [abs.(u_real[i] .- u_predict[i] ) for i in 1:3]
for i in 1:3
p1 = plot(xs, ts, u_real[i], st=:surface,title = "u$i, analytic");
p2 = plot(xs, ts, u_predict[i], st=:surface,title = "predict");
p3 = plot(xs, ts, diff_u[i],linetype=:contourf,title = "error");
plot(p1,p2,p3)
savefig("sol_u$i")
end
```