Discovering equations that govern wave breaking evolution using scientific machine learning

Artificial intelligence and machine learning are known to be excellent at empirical modelling of complex systems. These empirical models, however, usually can only provide limited physical explanations about the underlying systems. With a “knowledge discovery” scheme in machine learning, instead of being constrained by fitting the coefficients, can we now discover an equation that can shed light on the underlying physics? In this presentation, we will focus on a real fluid mechanics challenge as an example to demonstrate the potential of such a scheme – modelling wave breaking evolution.

In this ongoing study, we use symbolic regression to discover the equation that describes the wave breaking evolution from a large dataset of Direct Numerical Simulations of breaking waves. We found a new boundary equation that approximates the surface elevation (water-air interface) to evolve forward in time even during the breaking-in-progress stage, whereas traditional potential flow type equations will eventually become unstable when the overturning jet touches the crest. Unlike empirical models where the underlying dynamics are hidden in coefficients/matrixes, the physical meaning of each term of the discovered equation can be revealed successfully through math derivation and simulation. The new boundary equation suggests a new characteristic of breaking waves in deep water – a decoupling between the water-air interface and the fluid velocities. The current model is only limited to unidirectional spilling breaking waves in deep water but can be easily extended to accommodate more complex breaking behaviour.