SCALP

SCALP considers complex systems being governed by non-linear multiscale dynamics with non-local interactions between scales. These systems present extreme events in their dynamics as well as long-range dependences. Some examples of this kind of processes are fluid turbulence, ocean and atmosphere dynamics, stock markets, avalanche processes. They usually resist traditional analytical/simulation approaches, lacking a reliable and tractable physical model needed to perform any forecasting tasks. High dimensional chaotic systems may display a dynamics so intricated that no analytical theory is available, and the building of an explainable minimal model should provide insights. ML approaches are appealing in this context but require the design of new ML architectures exhibiting specific physics informed properties such as scales symmetries and conservation laws. Furthermore, observations are often scarce, eliminating de-facto too large architectures. Our aim is to develop deep but interpretable models with relevant scale symmetries and respecting physical conservations laws. As study cases we will be focusing on various multiscale dynamical models of turbulence (shell models, wave turbulence, fluid turbulence), chaotic models of atmospheric dynamics, and avalanche processes. Then, real data from observations, experiments and direct numerical simulations will be studied. The long-term impacts of SCALP concern contexts not limited to physics, where bigger non-interpretable networks is not the answer.