Thanks for your interest!
We are using various machine learning methods for improving the results of the newly published SINDy algorithm (here) and we need data!
SINDy stands for Sparse Identification of Nonlinear D(y)namics Video explanation and link to paper (not our work). We specifically want to improve its use for inferring dynamics after delay embedding (see the paper). We are using reinforcement learning and need a large number of dynamical systems of all sorts of dimensions to use as training data. We can't just pick random terms and coefficients since the vast majority diverge or converge rapidly and monotonically.
We are especially interested in chaotic systems or systems that (with the right initial conditions) explore a large region of state-space without being driven. We are not opposed to using a forcing term, its just that if we always use the same one then our machine learning algorithm will be biased towards it.
I found this site but it gives a 404 http://mathforum.org/library/view/16454.html
We can use anything between 1 and 10 dimensional systems up to 7th order polynomials and sine terms. Even a page from a book would be fine if we can get it as plain text and parse it. A database of python functions would be ideal.