agerlach

I'm not quite sure what you are looking for in a test problem. Are [these](https://www.sfu.ca/~ssurjano/optimization.html) applicable?

@ludoro Congrats on getting selected to GSoC again. I was happy to see it.

I have had good success using time-delay embeddings as observables. FYI, DynamicalSystems.jl has some delay embedding capabilities with algorithms for optimizing the embedding. See: [Delay Embeddings](https://juliadynamics.github.io/DynamicalSystems.jl/latest/embedding/reconstruction/)

I hacked around with it on my own before DataDrivenDiffEq was a thing. I agree completely regarding `DataSet`.

Thank you for the info.

I want to do optimization w/ reverse mode AD over the quadrature. I have an adjoint written that does ∫f(x,p)dx → ∫(∂/∂p f(x,p))dx. Not having individual convergence criterion for each...

> Why not do the integrals separately? The integrand is expense to compute. It is of the form `g(S(x))` where `S` is an ODE solve. If interested in more details...

@stevengj You are absolutely correct. Thank you. I miss characterized the behavior I saw. On second thought, the issue may be with respect to using constant tolerances for the quadrature...

Sign changes in coefficients `g.w` leads to `I=NaN` due to `Inf-Inf` https://github.com/JuliaMath/HCubature.jl/blob/66074a8b75f71066624517ea9a89b4f28e963b0f/src/genz-malik.jl#L150 I am happy to put together a PR to address this corner case, but it is unclear to...

On second thought short-circuiting would not be a good approach b/c integrand could be vector-valued mixing Inf and finite values.