Parameters estimation using NeuralPDE.jl is not working for PDEs

[OSHamouda]

Hello,
The inverse PINN problems handling partial differential equations does not work well as the code stops at the optimization (training ) step and the following error appears:
ERROR: type NamedTuple has no field layer_1

While it works well with ordinary differential equations such as Lorenz eqs example illustrated in the package's docs.
The used Julia version: 1.8.5

[ChrisRackauckas]

MWE?

[allen-adastra]

I've already ID'd the problem and the workaround:
#679

[OSHamouda]

I've already ID'd the problem and the workaround:
#679

I believe it's a different point here as the training process does not even start

[OSHamouda]

solved

[acaltran]

Hello,

I am relatively new to Julia and NeuralPDE. For learning purposes, I am trying to solve an inverse problem related to a simple Poiseuille flow. I seem to be encountering the same issue that was mentioned earlier. Unfortunately, I'm struggling to understand why this is happening.

I get the following error at the beginning of the solve process.

ERROR: type NamedTuple has no field layer_1

Could anyone explain how the issue was resolved previously, or possibly assist me in debugging my code?

The PDE that I'm working with is:

$$ \frac{d^2\tilde{w}}{dy^2}+\frac{1}{y}\frac{d\tilde{w}}{dy}+\tilde{w}_{source} = 0 \quad y \in [0, 1] $$

where

$$ \tilde{w}_{source} = \frac{\Delta P}{\mu l}R^2 $$

Here, $\tilde{w}(t)$ represents the flow velocity, and $\tilde{w}_{source}$ is the source parameter that I wish to optimize to match with the given noisy data.

using SciMLBase
using NeuralPDE, ModelingToolkit, Lux, Optimization, OptimizationOptimJL

using Plots
using Pipe

R = 10.0
l = 2.0
ΔP = 15
μ = 3.2

analytical = function (y::Real, R::Real, l::Real, ΔP::Real, μ::Real)
    ΔP / (4 * μ * l) * R^2 * (1 - y^2)
end

ndata = 10
noise_fact = 0.1
y_data = reshape(range(0, 1, ndata), 1, ndata)
w_data = analytical.(y_data, R, l, ΔP, μ) .+ noise_fact * analytical(0, R, l, ΔP, μ) * randn(size(y_data))

@parameters y, w̃ₛ
@variables w̃(..)

Dy = Differential(y)
Dyy = Differential(y)^2

eq = Dyy(w̃(y)) + 1 / y * Dy(w̃(y)) + w̃ₛ ~ 0

bcs = [w̃(1) ~ 0]

ε = 1e-9 #Avoir cost function evaluation at y=0
domains = [y ∈ (ε, 1)]

@named pde_system = PDESystem(eq, bcs, domains, [y], [w̃(y)], [w̃ₛ], defaults=Dict(w̃ₛ => 1.0))

chain = Chain(Dense(1, 4, Lux.σ), Dense(4, 1, Lux.σ))

additional_loss = function (phi, θ, p)
    sum(abs2, phi(y_data, θ) - w_data)
end

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

pinn_inv = NeuralPDE.PhysicsInformedNN(chain, QuasiRandomTraining(100), additional_loss=additional_loss, param_estim=true)
prob_inv = NeuralPDE.discretize(pde_system, pinn_inv)

res_inv = Optimization.solve(prob_inv, BFGS(); maxiters=5000)


y_plot = range(0, 1, 100)
plot(y_plot, analytical.(y_plot, R, l, ΔP, μ), label="analytical")
plot!(y_plot, @pipe(y_plot |> reshape(_, 1, length(_)) |> pinn.phi(_, res_inv.u)'), label="PINN")
plot!(y_data', w_data', seriestype=:scatter, label="data")

The st command provide the following output.

Status `~/infrastructure_ae/Project.toml`
  [b2108857] Lux v0.4.54
  [961ee093] ModelingToolkit v8.59.1
  [315f7962] NeuralPDE v5.7.0
  [7f7a1694] Optimization v3.15.2
  [36348300] OptimizationOptimJL v0.1.9
  [b98c9c47] Pipe v1.3.0
  [91a5bcdd] Plots v1.38.16
  [0bca4576] SciMLBase v1.93.0