Our motivation is to predict and understand complex mechanical systems, bearing numerical difficulties representative of real-world applications. Despite modeling improving accuracy and complexity, there are many situations where numerical simulations are not conceivable, or not affordable or not reliable at best.
Our group's motto is to leverage the information contained in various data sources in order to improve or discover our numerical models. This must be understood in a very broad sense, and the improvement term may cover several aspects, such as: - accuracy, - robustness,  - reliability, - certification, - efficiency, - scarcity, - versatility, - expressiveness, etc.
Dimensionality reduction, stochastic modeling and uncertainty quantification are the cornerstones of this open-minded approach. Methodological developments on all fronts, i.e. model reduction and high-dimensional approximation,  data assimilation and inference, statistical learning and information theory are keys to success for challenging ventures such as the prediction and control of turbulent flows.

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Motivation

Tools for numerical simulations have long become mainstream and ubiquitous in essentially every engineering domains. Despite their improving accuracy and complexity, there are however many situations where (direct) numerical simulations are not conceivable, or not affordable or not reliable at best. This difficulty becomes particularly stringent for "many-query" large-scale  problems: e.g., uncertainty quantification, robust optimization, inference, control, long-term health monitoring...

Computational barriers are many and include:

 - A poorly known environment to simulate. Real physical systems are generally incompletely characterized or subjected to irreducible variability, which makes their numerical modeling uncertain. Uncertainty sources include: geometry, external forcing, parameters, physical properties, operational conditions... In this framework, predictive validation and certification of the simulation is difficult due to the interplay of the numerous latent variables. As simulation tools are improving, both in terms of accuracy and complexity, it becomes more and more important to account for these uncertainties in order to fairly assess the validity of model-based numerical predictions, performing for instance global sensitivity analyses to hierarchize the importance of different sources of uncertainty.

 - Simulations of systems involving a large number of degrees-of-freedom are computationally intensive. They require massive resources in terms of time and hardware (HPC), often preventing a thorough study of the system under consideration. Typical of these are multi-scale systems such as turbulent flows, possibly with multi-physics (combustion, thermal transfers, flow-induced vibrations, acoustics, etc.).
 

 - Embedded hardware in autonomous systems rely on limited resources and communications and must then demonstrate computational autonomy. This constraint is particularly severe for environments with fast dynamics such as high-speed fluid flows. In this case, the control of the autonomous system in view of minimizing a cost objective by the embedded controller must be synthesized within a very short time, precluding the use of a sophisticated model.