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LuxDiffEq.jl
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LuxDiffEq.jl
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### A Pluto.jl notebook ###
# v0.19.5
using Markdown
using InteractiveUtils
# ╔═╡ a5aa719e-f1a4-11ec-24c1-cdf9b3ba173b
begin
using Lux
using DiffEqFlux, DifferentialEquations, Optimization, OptimizationOptimJL, Random
using Plots
using Gnuplot
end
# ╔═╡ 1a1f1c13-e418-475b-b4ec-db8bf3c15ea2
# Playing with NeuralODEs in Lux
# Started from: https://github.com/avik-pal/Lux.jl/blob/main/examples/NeuralODE/main.jl
# but then moved to https://diffeqflux.sciml.ai/dev/examples/neural_ode/
# ╔═╡ b64a6376-9b71-4b85-887f-f9f3e1bccd83
md"# Lorenz Attractor ODE spec"
# ╔═╡ 046b6282-b65d-434e-9916-3454921497dd
# hard-edged cubic spiral
begin
A=[-0.1 2.0 0; -2 -0.1 0; 0 0 0]
spiralu0=[2 0 0]
function s!(du,u,A,t)
du.=u.^3 * A
end
tspiral = (0.0,30)
odeSpiral=ODEProblem(s!,spiralu0,tspiral,A)
end
# ╔═╡ 7372e97b-dcdb-41b3-bb30-697b8c652482
# Lorenz attractor spec
begin
# From https://diffeq.sciml.ai/stable/analysis/uncertainty_quantification/#Example-3:-Adaptive-ProbInts-on-the-Lorenz-Attractor
function g(du,u,p,t)
du[1] = p[1]*(u[2]-u[1])
du[2] = u[1]*(p[2]-u[3]) - u[2]
du[3] = u[1]*u[2] - p[3]*u[3]
end
u0 = [-9.31058;-8.78892;28.7029] # start in stable left-hand node
#u0 = [1.0,0,0] # start on right hand lobe and jump straight to left
tspan = (0.0,30) # starts hopping between lobes @ t=15
datasize=500
tsteps = range(tspan[1], tspan[2], length = datasize)
ode_params = [10.0,28.0,8/3]
odeLorenz = ODEProblem(g,u0,tspan,ode_params)
end
# ╔═╡ 292484ee-70ad-4e90-ac71-83a90968afb1
prob_trueode=odeSpiral
# ╔═╡ 7bcdbdc4-95c7-4492-8898-7cedbd174335
sol_trueode=solve(prob_trueode,Tsit5(), saveat = tsteps)
# ╔═╡ 7d54362e-053c-403e-9ca0-43a6f10c3185
data_trueode=dropdims(Array(sol_trueode), dims=1) # spiral ends up with a singleton dimension?!
#data_trueode=Array(sol_trueode)
# ╔═╡ 809b5607-5a18-49bd-8b32-cd3c53d93307
begin
@gp sol_trueode.t sol_trueode[1,:] "w lp"
@gp :- sol_trueode.t sol_trueode[2,:] "w lp"
end
# ╔═╡ f4e1df28-652b-42de-835c-69a678d2b6dc
@gp sol_trueode[1,:] sol_trueode[2,:] "w lp"
# ╔═╡ 653a1bee-a90f-47a5-b77e-aa6f0721d738
md"# Neural ODE"
# ╔═╡ 127bfaa4-e619-40d4-bce0-de4e4069df2d
rng = Random.default_rng()
# ╔═╡ 483fd793-0a45-41fd-a29d-ed80ac5158af
#Lux.ActivationFunction(x -> x.^3)
dudt2 = Lux.Chain(
ActivationFunction(x -> x.^3),
Lux.Dense(3, 50, tanh),
# Lux.Dense(50,50,tanh),
# Lux.Dense(50,50,tanh),
# Lux.Dense(50,50,tanh),
Lux.Dense(50, 3))
# ,
# p -> solve(prob_trueode,Tsit5(),p=p)[1,:])
# ╔═╡ 51aae7db-45a2-48eb-b223-3c2ed4e82097
p = Lux.initialparameters(rng,dudt2)
# ╔═╡ ef49ad83-9e7a-4d07-bf9f-851289ddf4e7
st = Lux.initialstates(rng, dudt2)
# ╔═╡ f6a90f6a-9074-4969-92f0-d2fc37af60a9
prob_neuralode = DiffEqFlux.NeuralODE(dudt2, tspan, Tsit5(), saveat = tsteps)
# ╔═╡ 98685f21-7d18-41a1-92be-2d4a93ca1248
function predict_neuralode(p)
Array(prob_neuralode([2;0;0], p, st)[1])
end
# ╔═╡ 7f2aa049-38b8-4436-a04f-f639290e8b0b
function loss_neuralode(p)
pred = predict_neuralode(p)
loss = sum(abs, data_trueode .- pred)
return loss, pred
end
# ╔═╡ 1f020084-1d88-4bfd-9db0-74c24b140fdf
predict_neuralode(p)
# ╔═╡ 6c177fe8-0a99-4191-ad99-e0ea09181b99
md"""
# Training
"""
# ╔═╡ 8b94bcdb-2479-454b-ae34-95a2b51c553c
losses=[]
# ╔═╡ fd94353e-0698-4509-947e-fe542dfc7f1b
# JMF: currently this doesn't plot (during training) with Pluto
# Do not plot by default for the documentation
# Users should change doplot=true to see the plots callbacks
callback = function (p, l, pred; doplot = true)
# println(l)
append!(losses,l)
# plot current prediction against data
# plt = scatter(tsteps, data_trueode[1,:], label = "data")
# scatter!(plt, tsteps, pred[1,:], label = "prediction")
# display(plot(plt))
# @gp tsteps pred[1,:]
return false
end
# ╔═╡ bf838b92-8765-4cd9-a52b-f70357bc67fc
pinit = Lux.ComponentArray(p)
# ╔═╡ 71628110-bba1-4994-9e6d-f1a229dffafb
callback(pinit, loss_neuralode(pinit)...; doplot=true)
# ╔═╡ 71f7b01c-d75b-4234-b2c2-aa4711ef5cd4
# use Optimization.jl to solve the problem
adtype = Optimization.AutoZygote()
# ╔═╡ 518669fa-1f43-42ea-80e0-73986387706c
optf = Optimization.OptimizationFunction((x, p) -> loss_neuralode(x), adtype)
# ╔═╡ 34d92bcd-4c40-48a3-a433-36571e575485
optprob = Optimization.OptimizationProblem(optf, pinit)
# ╔═╡ 3305bc34-4897-4eb5-b7c5-081d2e9ac62b
md"# Train cell below here... ^_^"
# ╔═╡ dd6c05ba-1712-4ea3-a458-ee27b6eb18ec
result_neuralode = Optimization.solve(optprob,
ADAM(0.05),
callback = callback,
maxiters = 100)
# ╔═╡ 9b6fd73a-205d-413d-a63d-92611346c168
result_neuralode.u
# ╔═╡ 963cfb8d-3b3a-4a68-981e-36d2a00b96c3
predict_neuralode(result_neuralode.u)
# ╔═╡ 54a05048-14b5-49c3-968c-5aade6868826
losses
# ╔═╡ e0e5a6d2-7981-48ec-9ec9-e745337913f3
result_neuralode
# ╔═╡ 18264cb2-ec21-458b-9344-8bfe60dc61be
plot(losses)
# ╔═╡ ba12bfde-0500-484a-babb-bc5a71b90fb5
# ╠═╡ disabled = true
#=╠═╡
optprob2 = remake(optprob,u0 = result_neuralode.u)
╠═╡ =#
# ╔═╡ 76e664fd-ae4c-4817-ba17-0ad8b5dd7c0f
# ╠═╡ disabled = true
#=╠═╡
result_neuralode2 = Optimization.solve(optprob2,
Optim.BFGS(initial_stepnorm=0.01),
callback=callback,
allow_f_increases = false)
╠═╡ =#
# ╔═╡ 3fb61c90-7cf5-475a-8cf4-3a7ccd1b2150
# ╠═╡ disabled = true
#=╠═╡
callback(result_neuralode2.u, loss_neuralode(result_neuralode2.u)...; doplot=true)
╠═╡ =#
# ╔═╡ cf71eb69-2d19-4c63-8037-a787468dac58
# Time domain plot of the 1st variable
begin
pred = predict_neuralode(result_neuralode.u)
@gp tsteps data_trueode[1,:] "w lp title 'data1'"
@gp :- tsteps pred[1,:] "w lp title 'prediction1'"
@gp :- tsteps data_trueode[2,:] "w lp title 'data2'"
@gp :- tsteps pred[2,:] "w lp title 'prediction2'"
end
# ╔═╡ 343abd2d-3a42-4fdc-8298-abae876e7e37
# 2D plot of Lorenz phase space showing the lobes
begin
@gp data_trueode'[:,1] data_trueode'[:,2] "w lp title 'data'"
@gp :- pred'[:,1] pred'[:,2] "w lp title 'prediction'"
end
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
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Gnuplot = "dc211083-a33a-5b79-959f-2ff34033469d"
Lux = "b2108857-7c20-44ae-9111-449ecde12c47"
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OptimizationOptimJL = "36348300-93cb-4f02-beb5-3c3902f8871e"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
[compat]
DiffEqFlux = "~1.50.0"
DifferentialEquations = "~7.1.0"
Gnuplot = "~1.4.1"
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Optimization = "~3.7.0"
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# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
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