Optimizing parameters of ODE in DiffEqFlux: Not implemented: convert tracked Tracker.TrackedReal{Float64} to tracked Float64

Specific Domains Machine Learning
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1

My model:

using Random
using Flux, DiffEqFlux, DifferentialEquations

function model(dZ, Z, params, t)

    W0 = reshape(params[1:12], (1, 12))
    b0 = reshape(params[13:24], (1, 12))
    W1 = reshape(params[25:36], (12, 1))
    b1 = params[end]

    N = Integer(length(Z) / 4);

    X = Z[1:N];
    Y = Z[N + 1:2 * N];
    Vx = Z[2 * N + 1:3 * N];
    Vy = Z[3 * N + 1:4 * N];

    Vxdiff = broadcast(-, Vx, Vx');
    Vydiff = broadcast(-, Vy, Vy');
    Xdiff = broadcast(-, X, X');
    Ydiff = broadcast(-, Y, Y');

    R2 = Xdiff.^2 + Ydiff.^2;

    r = reshape(R2, (N * N, :))
    X0 = r * W0 .+ b0
    Z0 = max.(X0, 0)  
    X1 = Z0 * W1 .+ b1
    RR = reshape(X1, (N, N))

    dVx = -sum(Vxdiff .* RR, dims = 2) ./ N
    dVy = -sum(Vydiff .* RR, dims = 2) ./ N;

    dZ[:] = [reshape(Vx, (N, 1)); reshape(Vy, (N, 1)); dVx; dVy]  # ERROR LINE
end;


t = collect(0:0.1:10)

u0 = rand(20, 1)
tspan = (0.0, 1.0)
p_nominal = rand(37, 1);

prob = ODEProblem(model, u0, tspan, p_nominal)
data_sol = solve(prob, Tsit5(), saveat = 0.1)

p = rand(37, 1);
p = param(p)

function predict_rd()
    diffeq_rd(p, prob, Tsit5(), saveat = 0.1)
end

loss_rd() = sum(abs2, predict_rd() - data_sol);
print(loss_rd());

My error is

ERROR: LoadError: Not implemented: convert tracked Tracker.TrackedReal{Float64} to tracked Float64
Stacktrace:
 [1] error(::String) at .\error.jl:33
 [2] convert(::Type{Tracker.TrackedReal{Float64}}, ::Tracker.TrackedReal{Tracker.TrackedReal{Float64}}) at C:\Users\.julia\packages\Tracker\6wcYJ\src\lib\real.jl:39
 [3] setindex!(::Array{Tracker.TrackedReal{Float64},2}, ::Tracker.TrackedReal{Tracker.TrackedReal{Float64}}, ::Int64) at .\array.jl:767
 [4] macro expansion at .\multidimensional.jl:701 [inlined]
 [5] macro expansion at .\cartesian.jl:64 [inlined]
 [6] macro expansion at .\multidimensional.jl:696 [inlined]
 [7] _unsafe_setindex! at .\multidimensional.jl:689 [inlined]
 [8] _setindex! at .\multidimensional.jl:684 [inlined]
 [9] setindex! at .\abstractarray.jl:1020 [inlined]
 [10] model(::Array{Tracker.TrackedReal{Float64},2}, ::Array{Tracker.TrackedReal{Float64},2}, ::TrackedArray{…,Array{Float64,2}}, ::Float64) at d:\question\run.jl:34
 [11] ODEFunction at C:\Users\mzhen\.julia\packages\DiffEqBase\ZQVwI\src\diffeqfunction.jl:107 [inlined]
...

So the problem is here:

dZ[:] = [reshape(Vx, (N, 1)); reshape(Vy, (N, 1)); dVx; dVy]

How can I update dZ to avoid an error?

Thanks!

2

For me, changing the line to

dZ .= [reshape(Vx, (N, 1)); reshape(Vy, (N, 1)); dVx; dVy] |> collect

Seems to fix the problem.

Also, as a side note, you don’t need to use semicolons to end lines in julia.

3

I made some more changes so that your model will actually train. I tried to make comments every time that I made a change, but I may have missed a few. You might like to go through carefully and see what all of the changes are.

using Random
using Flux, DiffEqFlux, DifferentialEquations

function model(dZ, Z, params, t)

    W0 = reshape(params[1:12], (1, 12))
    b0 = reshape(params[13:24], (1, 12))
    W1 = reshape(params[25:36], (12, 1))
    b1 = [params[end]]  # If this is not an array, then training does not work for some reason.

    N = Integer(length(Z) / 4)

    X = Z[1:N];
    Y = Z[N + 1:2 * N];
    Vx = Z[2 * N + 1:3 * N];
    Vy = Z[3 * N + 1:4 * N];

    Vxdiff = broadcast(-, Vx, Vx');
    Vydiff = broadcast(-, Vy, Vy');
    Xdiff = broadcast(-, X, X');
    Ydiff = broadcast(-, Y, Y');

    R2 = Xdiff.^2 + Ydiff.^2;

    r = reshape(R2, (N * N, :))
    X0 = r * W0 .+ b0
    Z0 = max.(X0, 0)
    X1 = Z0 * W1 .+ b1
    RR = reshape(X1, (N, N))

    dVx = -sum(Vxdiff .* RR, dims = 2) ./ N
    dVy = -sum(Vydiff .* RR, dims = 2) ./ N;

    dZ .= [reshape(Vx, (N, 1)); reshape(Vy, (N, 1)); dVx; dVy] |> collect  # ERROR LINE
end


t = collect(0:0.1:10)

u0 = rand(20, 1)
tspan = (0.0, 1.0)
p_nominal = rand(37, 1)

prob = ODEProblem(model, u0, tspan, p_nominal)
data_sol = solve(prob, Tsit5(), saveat = 0.1)

p = rand(37, 1)
p = param(p)

function predict_rd()
    diffeq_rd(p, prob, Tsit5(), saveat = 0.1)
end

loss_rd() = sum(abs2, predict_rd() .- data_sol)  # Use .- here.
println(loss_rd())

params = Flux.Params([p])
opt = ADAM()
data = Iterators.repeated((), 20)
cb = () -> display(loss_rd())
Flux.train!(loss_rd, params, data, opt, cb=cb)
2 Likes
4

Thank, you, @JackDevine very much.
It works!

One question is not clear to me…

a = [1.0, 2, 3]
b = [4, 5, 6]
x1 = zeros(6)
x2 = zeros(6)
x3 = zeros(6)

x1[:] = [a; b]  #  Doesn't work with DiffEqFlux
x2[:] = vcat(a, b)  #  Doesn't work with DiffEqFlux
x3 .= [a; b] |> collect  #  Works with DiffEqFlux

println(x1 == x3)
println(x2 == x3)

Why can I use “|>” but can’t use “vcat(a, b)” or “[a; b]”? It looks like x1==x2==x3.

5

I think that the last comment in this issue might help you understand

So actually, the recommended way would be to use Tracker.collect. I am not a julia AD internals expert, so with any luck somebody who knows more will chime in.