In this talk I will present a few topics of recent interest that centre around the theme of “driven interfacial hydrodynamics”: fluid mechanical systems in which droplets and particles are self-propelled through interaction with the environment. I will also present some very recent work on using differentiable physics (a branch of physics-informed machine learning) to determine constitutive relations for highly plasticised metals.

This talk will contain elements of fluid dynamics, experimental mechanics, dynamical systems, statistical physics, and machine learning.

Rare and extreme events are notoriously hard to handle in any complex stochastic system: They are simultaneously too rare to be reliably observable in experiments or numerics, but at the same time often too impactful to be ignored. Large deviation theory provides a classical way of dealing with events of extremely small probability, but generally only yields the exponential tail scaling of rare event probabilities. In this talk, I will discuss theory, and algorithms based upon it, that improve on this limitation, yielding sharp quantitative estimates of rare event probabilities from a single computation and without fitting parameters. Notably, these estimates require the computation of determinants of differential operators, which in relevant cases are not traceclass and require appropriate renormalization. We demonstrate that the Carleman--Fredholm operator determinant is the correct choice. Throughout, I will demonstrate the applicability of these methods to high-dimensional real-world systems, for example coming from atmosphere and ocean dynamics.