Periodic boundary conditions isn't working.

[knuds]

Periodic boundary conditions is not working.

When I run the following code

using NeuralPDE, Lux, ModelingToolkit, Optimization, OptimizationOptimisers, Random, Plots
import ModelingToolkit: Interval

@parameters x,y,t
@variables u(..)

L=1
tmax=1
domains = [x ∈ Interval(-L, +L),
          y ∈ Interval(-L, +L),
      t ∈ Interval(0, tmax)]

Dx = Differential(x)
Dy = Differential(y)
Dxx = Differential(x)^2
Dyy = Differential(y)^2
Dtt = Differential(t)^2

eq=Dtt(u(x,y,t))~Dxx(u(x,y,t))+Dyy(u(x,y,t))

bcs=[u(x,y,0)~cos(x)*cosh(y),u(-L,y,t)~u(L,y,t),u(x,-L,t)~u(x,L,t), Dx(u(-L,y,t))~Dx(u(L,y,t)),Dy(u(x,-L,t))~Dy(u(x,L,t))]

in=length(domains)
n=9
chain = Lux.Chain(Dense(in, n, Lux.asinh), Dense(n, n, Lux.asinh),Dense(n, n, Lux.asinh), Dense(n, 1))

discretization = PhysicsInformedNN(chain, QuadratureTraining())

@named pdesystem = PDESystem(eq, bcs, domains, [x,y,t], [u(x,y,t)])

prob = discretize(pdesystem, discretization)
sym_prob = symbolic_discretize(pdesystem, discretization)
callback = function (p, l)
    println("loss: ", l)
    println(" pde: ", map(l_ -> l_(p), sym_prob.loss_functions.pde_loss_functions))
    println(" bcs: ", map(l_ -> l_(p), sym_prob.loss_functions.bc_loss_functions))
    println()
    return false
end

inter=200
res = Optimization.solve(prob, Adam(0.1); callback = callback, maxiters = inter)

I get output like:

loss: 13.413393568816456
 pde: [0.5311505128711426]
 bcs: [12.882243055945313, 0.0, 0.0, 0.0, 0.0]

With the periodic conditions all zero.

[knuds]

Symmetric conditions like: ,u(-x,y,t)~u(x,y,t),u(x,-y,t)~u(x,y,t) Does not work either.