Deep Learning for Physical Processes: An Application to Sea Surface Temperature Forecasting
Joint work with Emmanuel de Bezenac, Patrick Gallinari, LIP6, Université Pierre et Marie Curie, Paris VI, France

Modeling a physical phenomenon consists in finding the latent dynamic of an observation. The phys- ical approach to modeling consists in finding adequate analytic descriptions of the scientist’s prior knowledge of the underlying physical processes taking place. Typically, conservation laws, physical principles or phenomenological behaviors are formalized using differential equations. All non-negligible forces acting on the modeled quantities ought to be specified, along with their border conditions and various other parameters. Even in the case where the underlying physical processes are known and their associated analytic descriptions are sufficiently simple, this approach remains tedious and com- putationally demanding.
We want to explore an alternative to this classical modeling scheme. Given the large amount of data available, could modern ML techniques be used to learn modeling complex physical phenomena? Novel machine learning methods offer a complementary prior-agnostic approach where knowledge is not manually injected in the model but extracted from the data itself. Deep Learning has emerged as a very popular approach to deal with non-linear complex high dimensional data in domains where prior are unknown or difficult to describe, often achieving state of the art results where large quantities of data are available.

In the work we would like to present, we develop statistical methods for physical processes that exploit the massive amount of data available. We focus on a specific spatio-temporal problem: given sequences of images representing sea surface temperatures (SST) in time, we wish to predict future images. Forecasting SST is a hard problem due to many uncertain factors, but plays a significant role in various applications such as weather forecasting, or planning of coastal activities. This problem is typically approached from a physical point of view, where large coupled ocean-atmosphere systems are used to model the ocean’s dynamics and consequently to produce SST forecasts. Taking our inspiration from this approach along with recent deep learning methods for motion estimation and optical flow, we propose a novel approach to forecasting SST. We use a deep convolutional neural network (CNN) to estimate the underlying dynamics of the ocean and use a warping mechanism derived from the spatial transformer network (STN) to warp the image along the motion estimate. Further on, we provide arguments theoretically grounding our approach.