Cannot import ModelingToolkit: Interval, infimum, supremum

[finmod]

Loading the packages to run the updated PINNs example

using NeuralPDE, Flux, ModelingToolkit, GalacticOptim, Optim, DiffEqFlux
import ModelingToolkit: Interval, infimum, supremum

gives:

WARNING: could not import ModelingToolkit.Interval into Main
WARNING: could not import ModelingToolkit.infimum into Main
WARNING: could not import ModelingToolkit.supremum into Main

[ChrisRackauckas]

Remove import ModelingToolkit: Interval, infimum, supremum

[finmod]

then running the next Julia cell:

@parameters x
@variables p(..)
Dx = Differential(x)
Dxx = Differential(x)^2

α = 0.3
β = 0.5
_σ = 0.5
# Discretization
dx = 0.05
# here we use normalization condition: dx*p(x) ~ 1, in order to get non-zero solution.
#(α - 3*β*x^2)*p(x) + (α*x - β*x^3)*Dx(p(x)) ~ (_σ^2/2)*Dxx(p(x))
eq  = Dx((α*x - β*x^3)*p(x)) ~ (_σ^2/2)*Dxx(p(x))+dx*p(x) - 1.

# Initial and boundary conditions
bcs = [p(-2.2) ~ 0. ,p(2.2) ~ 0. , p(-2.2) ~ p(2.2)]

# Space and time domains
domains = [x ∈ Interval(-2.2,2.2)]

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

discretization = PhysicsInformedNN(chain,GridTraining(dx))

pde_system = PDESystem(eq,bcs,domains,[x],[p])
prob = discretize(pde_system,discretization)

#Callback function
cb = function (p,l)
    println("Current loss is: $l")
    return false
end

res = GalacticOptim.solve(prob,ADAM(0.1); cb = cb, maxiters=1500)
prob = remake(prob,u0=res.minimizer)
res = GalacticOptim.solve(prob,Optim.BFGS(initial_stepnorm=0.01);allow_f_increases=true, cb = cb, maxiters=400)

dx = dx/5
discretization = remake(discretization; strategy = NeuralPDE.GridTraining(dx), init_params =res.minimizer)
prob = NeuralPDE.discretize(pde_system,discretization)

res = GalacticOptim.solve(prob,ADAM(0.01); cb = cb, maxiters=1000)
prob = remake(prob,u0=res.minimizer)
res = GalacticOptim.solve(prob,Optim.BFGS(initial_stepnorm=0.01);allow_f_increases=true, cb = cb, maxiters=400)


dx= dx/5
discretization = remake(discretization; strategy = NeuralPDE.GridTraining(dx), init_params =res.minimizer)
prob = NeuralPDE.discretize(pde_system,discretization)

res = GalacticOptim.solve(prob,Optim.BFGS(initial_stepnorm=0.01);allow_f_increases=true, cb = cb, maxiters=400)
prob = remake(prob,u0=res.minimizer)
res = GalacticOptim.solve(prob,ADAM(0.001); cb = cb, maxiters=1000)

phi = discretization.phi

you get:

UndefVarError: Interval not defined

Stacktrace:
[1] top-level scope
@ In[3]:19
[2] eval
@ .\boot.jl:360 [inlined]
[3] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)
@ Base .\loading.jl:1094

[ChrisRackauckas]

Then you're not on the latest versions. This is a very recent change.

[finmod]

NeuralPDE v3.8.0 and ModelingToolkit v5.9.1

[ChrisRackauckas]

And Symbolics.jl?

[ChrisRackauckas]

NeuralPDE is v3.11.1.

[finmod]

Installing Symbolics.jl was incompatible with StructuralIdentifiability and SIAN. I removed them and updated. Now NeuralPDE is updating to v3.11.1 and ModelingToolkit to v5.18.1. This should do it.

[ChrisRackauckas]

Yup that should do it.

[finmod]

But you have to put import ModelingToolkit: Interval, infimum, supremum back in.

[ChrisRackauckas]

That's bad. Those should be exported.

[ChrisRackauckas]

what where would you need those functions?

[finmod]

In the PINNs FP example as well as in most others, there are several instances of these functions. I agree that the import should disappear.

# Space and time domains
domains = [x ∈ Interval(-2.2,2.2)]

and in here:

analytic_sol_func(x) = 28.022*exp((1/(2*_σ^2))*(2*α*x^2 - β*x^4))

xs = [infimum(d.domain):dx:supremum(d.domain) for d in domains][1]
u_real  = [analytic_sol_func(x) for x in xs]
u_predict  = [first(phi(x,res.minimizer)) for x in xs]

plot(xs ,u_real, label = "analytic")
plot!(xs ,u_predict, label = "predict")

[ChrisRackauckas]

I think we should just change the tutorial

[ChrisRackauckas]

xmin = -2.2
xmax = 2.2
domains = [x ∈ Interval(xmin,xmax)]

etc. Much nicer down the line. Requires less (unnecessary) machinery.

[ChrisRackauckas]

Version issue, fixed.