Physics-Informed Machine Learning:

CHECK-OUT this new Stochastic Environmental Research and Risk Assessment paper ! [Nony et al, SERRA 2023]

and this Journal of Computational Physics paper: [Lucor et al, JCP 2022]

The big data and machine learning revolution is gaining traction in the fluid mechanic community as it has changed the way turbulent data can be analyzed to more effectively extract knowledge from it. It becomes now possible to use deep learning to speedup or to (partly) substitute traditional fluid flow PDEs, which were expensive to solve. Nevertheless, generalization errors of those models are considerably improved if some "physics information" (in the form of invariant, first principles, symmetries, etc...) is included/enforced in order to regularize the training. Some effort is put to develop new ML methods along those lines, towards advanced methods for model-order reduction, system identification, PDE solver substitutes and turbulence closures.

Uncertainty quantification (UQ) for Computational Fluid Dynamics (CFD)

Thanks to the rapidly growing computational resources and improvements in numerical/experimental techniques, increasingly complex CFD problems are nowadays investigated. Assessing and optimizing the accuracy and reliability of numerical predictions has become a challenge of utmost importance. Due to the interdisciplinarity nature of UQ, this topic is also connected to the adjacent areas of statistics, high-performance computing, and the analysis of partial differential equations with random input data.

Data assimilation and inverse problems

The idea is to leverage the information contained in various data sources in order to improve our numerical models. The model is for instance complemented with data coming from additional physical/numerical experiments. The "data-enhanced" updated model can be made “data-frugal” thanks to specifics of the physical systems. Efficient data-driven methods scale with the effective dimension of the problem, as opposed to the ambient dimension, while naturally enjoying some robustness, a crucial aspect in practical applications.

Cardiovascular modeling and applications

Computational modeling of the function of the cardiovascular system has made great progress towards the development of patient-specific numerical aids to diagnosis, risk prediction, intervention and clinical treatment. The challenge is to combine medical image processing, high performance computational fluid dynamics simulation, and multi-scale modeling to simulate blood flow in a system plagued by numerous physiological and biological uncertainties: the human body.