Learning and Inference of Advective Fluid Transport in Geophysical Environments

Large scale Eulerian observations of atmospheric and oceanic systems have become ubiquitous, in part due to advances in satellite imagery and other similar techniques. Often times, these observations are gappy in time and space. This presents a unique challenge to learn and estimate the transport of quantities such as pollutants, debris, or marine nutrients to name a few, which are advected with the background flow as Lagrangian tracers. In this work, we present an approach to infer and predict of the underlying material transport characteristics given coarse resolution Eulerian data (such as satellite images). Our goals include: (i) inferring the flow physics and predicting the material transport in a geophysical system, given coarse resolution tracer field snapshots, and (ii) inferring fine resolution transport features from coarse resolution data. To achieve these, we use and extend memory based neural networks (such as RNNs and LSTMs) and other ideas from the field of deep learning. We specifically focus on the methods that can leverage our knowledge of the physical constraints that the results must satisfy (e.g. mass conservation) to critically reduce the ML search space. This allows us to infer fluid flow physics and dynamics along with the corresponding material transport predictions, only from sparse, coarse resolution data. The developed theory, methods, and computational architectures are validated and tested on a variety of test cases.