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ACUMES Research team

Analysis and Control of Unsteady Models for Engineering Sciences

Team presentation

The project focuses on the analysis and optimal control of classical and non-classical evolutionary PDEs systems arising in a variety of applications, ranging from fluid-dynamics and structural mechanics to traffic flow and biology.  The complexity of the involved dynamical systems is expressed by multi-scale, time-dependent phenomena subject to uncertainty, which can hardly be tackled using classical approaches, and require the development of unconventional techniques.

Research themes

The project develops along the following three axes,  which are common to the specific problems treated in the applications.

  • Dynamics of novel PDE models. Evolutionary PDEs, mainly of hyperbolic type, appear classically in purely macroscopic models, but they are not able to account for particular phenomena related to specific interactions occurring at lower (possibly micro) level. These phenomena can be of greater importance when dealing with particular applications, where the "first order" approximation given by the purely macroscopic approach reveals to be inadequate. Therefore, we aim at completing macroscopic models with information on the dynamics at the small scale / microscopic level. This can be achieved through several techniques: micro-macro couplings, non-local flows, measure-valued solutions, mean-field games, etc.
  • Accounting for uncertainty in PDE simulations and control. Uncertainty quantification and analysis is an issue  of utmost importance for engineering applications. Uncertainty appears at several stages of the modeling/transfer process: data assimilation, model design and calibration, optimization subject to the model, etc.
    For the applications targeted in this project, we address uncertainty in parameters and initial-boundary data dealing with model calibration and validation, as well as  robust design and control.
  • Optimization and control algorithms for systems governed by PDEs. We focus on the methodological development and analysis of optimization algorithms and paradigms for PDE systems in general, keeping in mind  our privileged domains of application in the way the problems are mathematically formulated. More precisely, we deal with hierarchical methods, multi-objective descent algorithms, games for ill-posed problems, etc.

International and industrial relations

The team has several established collaborations with research laboratories (UC Berkeley,LIRIMA, Universities of Brescia an Milan in Italy, Universities of Mannheim and Wurzburg in Germany, etc.) and R&D industries (Arcelor Mittal, IBM, ONERA, etc.)

 

 

Keywords: Evolutionary PDEs Optimal control Uncertainty quantification Finite volume methods Optimization paradigms