Why is this scenario of function parameter estimation acting strangely? Using LsqFit

General Usage
2

well seems to be related to this thread. Note that Levenberg Marquardt is not the robustest Method for such kind of problems (multiple local minima).

Optim.jl provides a simple SA-Optimizer which tend to be more robust for this task

using Optim

loss(u) = sum((data .- model(t,u)).^2)
res =  optimize(loss, p0_bounds, SimulatedAnnealing())

# Plot result
scatter(t, data)
plot!(t, model(t, Optim.minimizer(res)))

Or you can try the awesome BlackBoxoptim.jl

EDIT: To elaborate a bit on this:
By simply plotting the value of loss(u) around the p₀ you can visualize how challenging your problem actually is:
image

you can see multiple local minima next to the global one

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