Learning fluid dynamical statistics using stochastic neural networks

Many practical problems in fluid dynamics demand an empirical approach, where statistics estimated from data inform understanding and modelling. In this context data-driven probabilistic modelling offers an elegant alternative to ad hoc estimation procedures. Probabilistic models are useful as emulators, but also offer an attractive means of estimating particular statistics of interest. In this paradigm one can rely on proper scoring rules for model comparison and validation, and invoke Bayesian statistics to obtain rigorous uncertainty quantification. Stochastic neural networks provide a particularly rich class of probabilistic models, which, when paired with modern optimisation algorithms and GPUs, can be remarkably efficient. We demonstrate this approach by learning the single particle transition density of ocean surface drifters from decades of Global Drifter Program observations using a Bayesian mixture density network. From this we derive maps of various displacement statistics and corresponding uncertainty maps. Our model also offers a means of simulating drifter trajectories as a discrete-time Markov process, which could be used to study the transport of plankton or plastic in the upper ocean.