AI can be used for finding structures in data from scratch, i.e. without knowing about them beforehand. One might wonder whether AI can be used to decide whether a dynamical system is integrable or not? In this talk, I report on how we can set up machines to successfully search for the Lax pair and Lax connection in some classical examples. We shall also see how symbolic regression can be used to render the output interpretable for a physicist.

I briefly give an overview on the key ML frameworks involved in this analysis (neural networks, auto-differentiation, representation learning). This talk is mainly based on 2103.07475, and further related work can be found here 2104.14444, 2003.13679.