The PO seems to be especially interested in dynamical systems. `
`Here is an article where a deep learning Long Short-Term Memory (LSTM) network (see this reference for the architecture) can be used to reconstruct an underlying dynamical system from a set of data points without prior assumptions.
It should be pointed out that most models generated by deep learners are not easy to understand. However, recent works goes in the direction of explainability across all Machine Learning, and there are tools even for deep networks (there is a substantil literature in this space, and also tools. For instance, if someone likes Pytorch, as I do, for his/her experiments, one may leverage SHAP or other tools, see this basic article here .
So, summing up: a researcher could use a recurrent deep network to ' interpolate" data points and generate a non-linear dynamics, then leverage some explainer to extract a simplified and more human digestible model. As one can run all of the above in a distributed fashion, this sequence would provide a great help both in creating models, and testing out hypothesis.
