Spoken language is characterised by a high-dimensional and highly variable set of physical movements that unfold over time. What are the fundamental dynamical principles that underlie this signal? In this study, we demonstrate the use of physics- informed machine learning (sparse symbolic regression) for discovering new dynamical models of speech articulation. We first demonstrate the model discovery procedure on simulated data and show that the algorithm is able to discover the original model with near-perfect accuracy, even when the data contain extensive variation in duration, initial conditions and tar- get positions, as well as in the presence of added noise. We then demonstrate a proof-of-concept applying the same technique to empirical data, which reveals a small set of candidate dynamical models with increasing levels of complexity and accuracy.