Probably user error: sciML_train func running but not optimizing #528
Description
Hi all, as posted here,
My executions of DiffEqFlux.sciml_train are not optimizing but yet are iterating for the full amount without error. By not optimizing, I mean that for whatever random initial parameters I feed for a fitting example, the loss function does not change at each iteration and the final minimizers are the initial parameters. This remains true despite changing the learning rate for Adam, the number of iterations, the solver entirely (I also tried BFGS and SOSRI) or sensealg=ForwardDiffSensitivity().
I am using the standard loss(abs2, predicted - observed) and based on the initializations I randomize with I see significant variations in the loss which makes me think for some initial conditions some improvement should be possible. Previously, I have optimized identical systems with higher dimensions and terrible data with matlab’s fmincon().
All this leads me to believe I am making some novice error which is likely given I am new to julia and DiffEqFlux. Any help would be much appreciated. Note, I did just update everything, restarted atom and found the same problem.
First, I generate the model problem,
##
using Plots, Random
using DifferentialEquations, Flux, Optim, DiffEqFlux, DiffEqSensitivity
## Define GLV and generate synthetic data from defined parameters
tsteps = 24
n=3
function gLV!(dx,x,p,t)
# Weird ReverseDiff (AD) bug
if (typeof(p) != Array{Float64,1}) #&& (typeof(p) != SciMLBase.NullParameters)
p=p.value
end
# unpack params
n = length(x)
mu = p[1:n]
A = Array{Float64,2}(undef,3,3)
for i=1:n; A[:,i] = p[n*i + 1: n*(i+1)]; end
dx .= x.*(mu + A*x)
if any(x .> 100.0) # no cc catch
dx .= 0
end
end
condition(u,t,integrator) = any(u .< 1e-8) #|| any(u .> 10)
function affect!(integrator)
integrator.u[integrator.u .< 1e-8] .= 0
end
cb = ContinuousCallback(condition,affect!)
mu_true = [0.4; 0.8; 0.2].*0.1
A_true = [-1.5 0.5 -0.2; -0.7 -1.3 0.1; 0.8 -0.2 -0.9]
p_true = [mu_true; A_true[:]]
x0 = [0.1; 0.1; 0.1].*0.1
tspan = (0.0, 144.0)
prob = ODEProblem(gLV!, x0, tspan)
sol = DifferentialEquations.solve(prob, Tsit5(), p=p_true, saveat=tsteps, callback=cb)
syndata = Array(sol) + 0.002*randn(size(Array(sol)))
plot(sol, alpha=0.3)
Plots.scatter!(sol.t, syndata')
title!("Definite")
After making the model problem and generating some noisy data with the true parameters, I then initialize random parameters, define a loss function and call sciml_train.
## Random Initialize
mu_init = 0.1*rand(n)
A_init = -1*rand(n,n)
p_init = [mu_init; A_init[:]]
## Optimization and Fitting
i=0
function loss(p_curr)
global i
i+=1
sol = DifferentialEquations.solve(prob, Tsit5(), p=p_curr, saveat=tsteps, callback=cb)
loss = sum(abs2, Array(sol) - syndata)
print("\n Loss of ",loss, " on iteration ",i)
return loss, sol
end
result_ode = DiffEqFlux.sciml_train(loss, p_init,
ADAM(0.1),
maxiters=50)
print("\n")
print("\n p_init:", round.(p_init,digits=4))
print("\n p_optm:", round.(result_ode.minimizer,digits=4))
which outputs for a given initialization one score repetitively and then prints the same two sets of parameters, like so:
0.013182825077950067 on iteration 1
Loss of 0.013182825077950069 on iteration 2
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p_init:[0.0621, 0.0467, 0.0351, -0.7881, -0.9748, -0.8404, -0.6985, -0.387, -0.8855, -0.6415, -0.5578, -0.2624]
p_optm:[0.0621, 0.0467, 0.0351, -0.7881, -0.9748, -0.8404, -0.6985, -0.387, -0.8855, -0.6415, -0.5578, -0.2624]