Learning large ODE systems from data

In the recent years, Sparse Identification of Nonlinear Dynamical systems (SINDy) has become quite popular to learn ODE systems (ODEs) from data. SINDy is basically regularized regression on ODEs coefficients. The PySINDy package documentation contains plenty of examples and extensions to the original algorithm.

Personally, I have found SINDy quite unstable for medium-sized ODEs (10-100 variables) and noisy data, unless data is very dense with respect to time. I was wondering if anyone has experience scaling to medium or large ODEs using Stan or have any valuable pointers? One useful trick might be to perform a change of coordinates using an autoencoder.