Abstract
The Sea Surface Temperature (SST) plays a significant role in analyzing and assessing the dynamics of weather and also biological systems. It has various applications such as weather forecasting or planning of coastal activities. On the one hand, standard physical methods for forecasting SST use coupled ocean- atmosphere prediction systems, based on the Navier-Stokes equations. These models rely on multiple physical hypotheses and do not optimally exploit the information available in the data. On the other hand, despite the availability of large amounts of data, direct applications of machine learning methods do not always lead to competitive state of the art results. Another approach is to combine these two methods: this is data-model coupling. The aim of this paper is to use a model in another domain. This model is based on a data-model coupling approach to simulate and predict SST. We first introduce the original model. Then, the modified model is described, to finish with some numerical results.
Highlights
The general task of this assignment could have been guessed from the title "Partial differential equations for oceanic artificial intelligence"
The idea was to use artificial intelligence tools to determine the Sea Surface Temperature (SST) of a given oceanic zone. This had already been done in Bezenac et al [1]. What they exactly did is using a Convolutional Neural Network (CNN) and a transport equation to predict the evolution of the field of surface temperature for a few days
The CNN was used to identify and predict the velocity field used in the transport equation
Summary
The general task of this assignment could have been guessed from the title "Partial differential equations for oceanic artificial intelligence". Machine learning has been used in this context by Zhang and Lin [7] and could identify the non-linear terms present in the output of an hydrodynamic model In this case, they did not use a Neural Network, but sophisticated parameters identification tools such as stochastic gradient descent and LASSO objective function. Another interesting approach was the one of Chen et al [6] and Ruthotto and Haber [5] Their idea was to mimick the behavior of a Neural Network by differential equations, ordinary in the first paper and partial in the second. The interest of this approach would be to use the computationnally efficient tools that exists for identifying parameters in differential equations to replace the back propagation in Neural Networks. The idea was that the PDE was close enough to the physics of our problem to be efficient, and that the ODEs could be fitted in order to represent the phenomenon not taken into account in the PDE
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