ANR SCALES

In nature, a large number of systems and processes present non-linear and multi-scale structures and behaviors, and are thus considered as complex systems. Because of these properties, models aiming at describing or predicting the behavior of complex systems need to take into account high-order statistics in a whole range of scales. In this project, I propose:

1) to develop a new statistical description of multi-scale coupling and interactions based on Information Theory, which can be directly linked to complexity and then to the structure and state of this kind of systems. Such a framework will be able to characterize high order statistics across scales, and so, non-linear multi-scale behaviors. I will focus on the characterization of 1) scale invariance and long range dependencies and 2) causality interactions (in the Wiener-Granger sense) between scales.

2) the combination of this statistical characterization with Artificial Intelligence in order to develop new multi-scale learning-based approaches for modeling complex systems. First, a review of adapted metrics based on the developed Information Theory framework will be done. Second, they will be tested on different models such as variational and Neural ODE ones. Finally, for a chosen model and metric, the architecture of the model will be adjusted to deal with complex systems in an efficient way.

As a case study, I focus on the characterization and modeling of ocean surface dynamics since they present non-linear and multi-scale behaviors. Furthermore, ocean surface dynamics is a major issue in oceanographic and climate research, and its correct modeling is of high importance for answering to a large number of ecological issues. Thus for example, it is well known that these dynamics impact marine biodiversity. They also drive ocean-atmosphere interactions that influence the climate. So, this project is engaged in addressing part of the H2050 challenges pointed out by our society. Despite the fact of focusing on ocean dynamics as a case of study, I would like to remark that the proposed framework can be later extended to study other kind of complex systems.