periodic boundary conditions about neuralpde.jl HOT 2 CLOSED

#Example,  2D Poisson equation with periodic boundary conditions
@parameters x y θ
@variables u(..)
@derivatives Dxx''~x
@derivatives Dyy''~y

# 2D PDE
eq  = -(Dxx(u(x,y,θ)) + Dyy(u(x,y,θ))) ~ x*sin(5.0*π*y)+exp(-((x-0.5)^2+(y-0.5)^2)/0.02)

#Initial and boundary conditions
bcs = [#Dirichlet boundary
       u(x,0,θ) ~ 0.,
       u(x,1,θ) ~ 0.,
       #Periodic boundary
       u(0,y,θ) ~ u(1,y,θ)]

#Space and time domains
domains = [x ∈ IntervalDomain(0.0,1.0),
          y ∈ IntervalDomain(0.0,1.0)]
#Discretization
dx = 0.1


#Neural network and optimizer
chain = FastChain(FastDense(2,16,Flux.σ),FastDense(16,16,Flux.σ),FastDense(16,1))

discretization = NeuralPDE.PhysicsInformedNN(dx,chain)

pde_system = PDESystem(eq,bcs,domains,[x,y],[u])
prob = NeuralPDE.discretize(pde_system,discretization)

res = GalacticOptim.solve(prob,Optim.BFGS(); cb = cb, maxiters=1000)
phi = discretization.phi

xs,ys = [domain.domain.lower:dx/10:domain.domain.upper for domain in domains]
u_predict = reshape([first(phi([x,y],res.minimizer)) for x in xs for y in ys],(length(xs),length(ys)))

plot(xs, ys, u_predict, st=:surface)