# Help with modifying SciML Missing Physics UDE example

**URL:** <https://discourse.julialang.org/t/help-with-modifying-sciml-missing-physics-ude-example/104773>\
**Category:** Modelling & Simulations\
**Tags:** question\
**Created:** [October 9, 2023, 10:40pm UTC](https://discourse.julialang.org/t/help-with-modifying-sciml-missing-physics-ude-example/104773 "2023-10-09T22:40:04Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![BenWhip](https://avatars.discourse-cdn.com/v4/letter/b/a3d4f5/32.png) [@BenWhip](https://discourse.julialang.org/u/BenWhip)\
**Post date:** [October 9, 2023, 10:40pm UTC](https://discourse.julialang.org/t/help-with-modifying-sciml-missing-physics-ude-example/104773/1 "2023-10-09T22:40:04Z")

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Hello all,

I’ve made some minor modifications to the code from [Automatically Discover Missing Physics by Embedding Machine Learning into Differential Equations · Overview of Julia's SciML](https://docs.sciml.ai/Overview/stable/showcase/missing_physics/)

My goal is to expose unknown parameters and known parameters in the UDE so that unknown parameters can be trained and known parameters can be utilized.

The top level error is: “LoadError: type NamedTuple has no field mech\_params”

1. Am I taking an appropriate direction to implement my goal, or is there a better paradigm in the SciML framework?
2. If this is a reasonable direction, in what directions should I make changes to the code?

Thank you in advance for your assistance.

A reduced working example follows. The stacktrace is fairly long, so I haven’t included it:

```julia
# SciML Tools
using OrdinaryDiffEq, ModelingToolkit, DataDrivenDiffEq, SciMLSensitivity, DataDrivenSparse
using Optimization, OptimizationOptimisers, OptimizationOptimJL

# Standard Libraries
using LinearAlgebra, Statistics

# External Libraries
using ComponentArrays, Lux, Zygote, Plots, StableRNGs
gr()

# Set a random seed for reproducible behaviour
rng = StableRNG(1111)

function lotka!(du, u, p, t)
    α, β, γ, δ = p
    du[1] = α * u[1] - β * u[2] * u[1]
    du[2] = γ * u[1] * u[2] - δ * u[2]
end

# Define the experimental parameter
tspan = (0.0, 5.0)
u0 = 5.0f0 * rand(rng, 2)
p_ = [1.3, 0.9, 0.8, 1.8]
prob = ODEProblem(lotka!, u0, tspan, p_)
solution = solve(prob, Vern7(), abstol = 1e-12, reltol = 1e-12, saveat = 0.25)

# Add noise in terms of the mean
X = Array(solution)
t = solution.t

x̄ = mean(X, dims = 2)
noise_magnitude = 5e-3
Xₙ = X .+ (noise_magnitude * x̄) .* randn(rng, eltype(X), size(X))

plot(solution, alpha = 0.75, color = :black, label = ["True Data" nothing])
scatter!(t, transpose(Xₙ), color = :red, label = ["Noisy Data" nothing])

rbf(x) = exp.(-(x .^ 2))

# Multilayer FeedForward
const U = Lux.Chain(Lux.Dense(2, 5, rbf), Lux.Dense(5, 5, rbf), Lux.Dense(5, 5, rbf),
              Lux.Dense(5, 2))
# Get the initial parameters and state variables of the model
p, st = Lux.setup(rng, U)
const _st = st

p_full = ComponentVector(dd_params=p, mech_params=[1.0,],known_params=[1.8,])

# Define the hybrid model

function ude_dynamics!(du, u, p, t)

    p_mech = p.mech_params
    p_true = p.known_params
    p_nn = p.dd_params

    û = U(u, p_nn, _st)[1] # Network prediction
    du[1] = p_mech[1] * u[1] + û[1]
    du[2] = -p_true[4] * u[2] + û[2]
end

prob_nn = ODEProblem(ude_dynamics!, Xₙ[:, 1], tspan, p_full)

function predict(θ, X = Xₙ[:, 1], T = t)
    _prob = remake(prob_nn, u0 = X, tspan = (T[1], T[end]), p = θ)
    Array(solve(_prob, Vern7(), saveat = T,
                abstol = 1e-6, reltol = 1e-6,
                sensealg=QuadratureAdjoint(autojacvec=ReverseDiffVJP(true))))
end

function loss(θ)
    X̂ = predict(θ)
    mean(abs2, Xₙ .- X̂)
end

adtype = Optimization.AutoZygote()
optf = Optimization.OptimizationFunction((x, p) -> loss(x), adtype)

optprob = Optimization.OptimizationProblem(optf, p_full)
res1 = Optimization.solve(optprob, ADAM(), maxiters = 5000)

optprob2 = Optimization.OptimizationProblem(optf, res1.u)
res2 = Optimization.solve(optprob2, Optim.LBFGS(), maxiters = 1000)

```

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 16, 2023, 10:58am UTC](https://discourse.julialang.org/t/help-with-modifying-sciml-missing-physics-ude-example/104773/2 "2023-10-16T10:58:00Z")

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> [@BenWhip](#):
>
> ```julia
> p_full = ComponentVector(dd_params=p, mech_params=[1.0,],known_params=[1.8,])
> 
> ```

Did you try converting `p` to a ComponentArray first?

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<div class="post-metadata">

**Author:** ![BenWhip](https://avatars.discourse-cdn.com/v4/letter/b/a3d4f5/32.png) [@BenWhip](https://discourse.julialang.org/u/BenWhip)\
**Post date:** [October 20, 2023, 10:04pm UTC](https://discourse.julialang.org/t/help-with-modifying-sciml-missing-physics-ude-example/104773/3 "2023-10-20T22:04:02Z")

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That, with a few other minor changes, fixed my problem. Thanks.