Portfolio of team DATAFLOT
DAta science, TrAnsition, Fluid instabiLity, contrOl, Turbulence

Article: Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review

Sibo Cheng, César Quilodrán-Casas, Said Ouala, Alban Farchi, Che Liu, Pierre Tandeo, Ronan Fablet, Didier Lucor, Bertrand Iooss, Julien Brajard, Dunhui Xiao, Tijana Janjic, Weiping Ding, Yike Guo, Alberto Carrassi, Marc Bocquet, Rossella Arcucci. Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review. IEEE/CAA Journal of Automatica Sinica, Vol: 10, Issue: 6, June 2023. DOI: 10.1109/JAS.2023.123537

• HAL: hal-04039094
• PDF version of the article (from HAL)

Context

This methodological 2023 review article published in the IEEE/CAA Journal of Automatica Sinica was initiated by Sibo Cheng, ex-PhD student from LIMSI lab (working on data assimilation under the supervision of Didier Lucor) during his time as research associate in the Departement of Computing, Faculty of Engineering at Imperial College and now tenure-track professor at Ecole des Ponts, ParisTech. This review paper was written in collaboration with 17 esteemed academics and industry professionals from 6 countries, including contributions from around ten different laboratories including the LISN with experts in deep learning, uncertainty quantification and data assimilation. It filled a gap in a interdisciplinary literature by highlighting the strong connections and complementarity between different scientific communities and numerical methods from uncertainty quantification (UQ), data assimilation (DA), and machine learning (ML) in the modeling of dynamical systems.

Contribution

Uncertainty quantification and Data Assimilation are more and more used in analysing and reducing error propagation in high-dimensional spatial-temporal dynamics such as the ones for instance encountered in computational fluid mechanics. Recently, much effort has been given in combining DA, UQ and ML techniques as substantial mathematical similarities exist between these disciplines. These research efforts seek to address some critical challenges in high-dimensional dynamical systems, including but not limited to dynamical system identification, reduced order surrogate modelling, error covariance specification and model error correction. A large number of developed techniques and methodologies exhibit a broad applicability across numerous domains, resulting in the necessity for a comprehensive guide.

This paper provides the first overview of the state-of-the-art researches in this interdisciplinary field, covering a wide range of applications. The paper has a special focus on how ML methods can overcome the existing limits of DA and UQ, and how the different techniques maybe combined and hybridized. DATAFLOT/LISN contribution was more centered on the theory of the UQ and ML topics in particular with uncertainty quantification of ML techniques themselves such as UQ of deep neural networks (Bayesian Neural Networks, Monte-Carlo Dropouts, Ensemble Models, etc.).

A strong contribution is to show how these hybrid models provide strengths in interpretability and noise reduction. This review includes a range of challenging high dimensional, multimodal and multi-scale systems applications including Numerical Weather Prediction (NWP), environmental modelling and Computational Fluid Dynamics (CFD). The development trends and future challenges of this fast-growing field are also investigated.

Impact

Since its very recent publication in June 2023 (not even one year ago as of this writing), the paper has been cited 66 times according to Google Scholar and downloaded 2456 times from the IEEE/CAA Journal of Automatica Sinica (journal with an impact factor of IF=11.8 and a 17.6 CiteScore-Scopus).

This paper provides the first overview of state-of-the-art researches in an interdisciplinary field, covering a wide range of applications. This review is aimed at ML scientists who attempt to apply DA and UQ techniques to improve the accuracy and the interpretability of their models, but also at DA and UQ experts who intend to integrate cutting-edge ML approaches to their systems.

Organization of a Euromech workshop

The Euromech Colloquium was a three-day international workshop dedicated to Machine learning methods for the prediction and control of separated turbulent flows. It has been organized in the Conservatoire National des Arts et Métiers in Paris in June 2021. This event was supported by Euromech and has benefited from its financial support.

The workshop has attracted about 75 international participants. The programme featured about 30 talks and 6 invited keynotes:

• Prof. Luca Biferale (Dept. of Physics, University of Rome, Italy)
• Prof. Erik M. Bollt (Dept. of Electrical and Computer Engineering, Clarkson University, USA)
• Prof. Karthik Duraisamy (Computational Aerosciences Lab, U. Michigan, USA)
• Prof. Angelo Iollo (University of Bordeaux and Inria Bordeaux, France)
• Prof. Themis Sapsis (Dept. of Mechanical Engineering, Massachusetts Institute of Technology, USA)
• Prof. Weiwei Zhang (School of Aeronautics, Northwestern Polytechnical University, P. R. China)

The workshop was devoted to the following topics:

• Active and closed-loop control for flow control (noise mitigation, transition delay, drag reduction, mixing enhancement, etc.)
• Model-predictive control, genetic programming, reinforcement learning, ...
• Spectral analysis (operator-theoretic tools, generalized stability analysis, etc.)
• Dimensionality reduction, manifold learning, kernel methods
• Deep learning, data-mining, Physics-informed machine learning, ...
• Estimators / observers, data-assimilation
• Sensors and actuators placement

Context

Some members of the Dataflot team are actively working on data-based methods for Physics-related challenges in general, and fluid flows in particular. This research activity has been supported through several ANR grants over the last years (ANR Flowcon (2017-2019), ANR Speed).

The need for a such a workshop was partly motivated by observing that the steady rise of machine learning techniques, combined with the availability of affordable sensor arrays, has had a transformative impact in a large number of scientific fields. In particular, with the dramatic increase in data accessibility and computational power, traditional model-based approaches in engineering are giving way to a data-enhanced paradigm. Prediction and control of turbulent flows, a challenging area of engineering sciences, are no exception in this respect. Despite early attempts, the successful control of such complex systems by machine learning techniques raises specific issues such as weak observability or an exhaustive range of temporal and spatial scales. Moreover, the effective incorporation of knowledge about the physical system, such as symmetries, invariances or conservation laws, into the learning process is far from trivial.

Nonetheless, recent success of machine learning techniques in the prediction of chaotic dynamical systems and control of highly nonlinear flows has fueled a great many research efforts and has shown that progress in this field critically relies on an interdisciplinary skill set, ranging from applied mathematics and machine learning to physics, from computer science to experimental methods.

Contribution of Dataflot/LISN

Dataflot members were instrumental in setting-up and organizing this event. Lionel Mathelin was the general chair of the conference. Onofrio Semeraro has actively contributed to defining the scientific program and was a member of both the scientific and organizing committee. Alessandro Bucci, a then senior postdoc student in the team, was also a member of both the scientific and organizing committee.

Impact

The aim of the workshop was to bring together control practitioners, fluid dynamicists and machine learning experts to critically review recent developments in the field and identify both opportunities and challenges in using machine learning techniques for high-dimensional physical systems. The workshop was meant to act as a forum for exchanging ideas and as an occasion to learn and discuss.

Altogether there were 77 participants from 12 countries and 34 presentations, including 6 keynotes. The final report can be found here.

This workshop has significantly contributed to advertise some of the activities of the Dataflot team for the machine learning and data-science international community. It has provided a high-visibility stage, favoring subsequent recognition and contacts abroad for the team members.

Article: A simple model for arbitrary pollution effects on rotating free-surface flows

Antoine Faugaret, Yohann Duguet, Yann Fraigneau, Laurent Martin Witkowski A simple model for arbitrary pollution effects on rotating free-surface flows. Journal of Fluid Mechanics, Vol: 935, Issue: A2, 2022. [DOI: 10.1017/jfm.2021.980 ]

• HAL: hal-03695092
• PDF version of the article

Context :

In an experimental context, the contamination of an air–liquid interface by ambient pollutants can strongly affect the dynamics and the stability of a given flow. In some configurations, the interfacial flow can even be blocked by surface tension effects. In this work, a cylindrical free-surface flow driven by a slow rotating disc is considered as a generic example of such effects and is investigated both experimentally and numerically. We have suggested a simple numerical model, without any superficial transport of the pollutants, adaptable into any code for single-phase flows. For a geometrical aspect ratio of 1/4, known to display ambiguous behaviour regarding stability thresholds, the modal selection as well as a nonlinear stability island found in the experiments are well reproduced by the model, both qualitatively and quantitatively. The robustness of the model has also been validated by replacing the radial velocity profile by a more accurate experimental fit, with very little influence on the stability results.

One a more general note, this article illustrates the complementarity between experiments and numerical simulations, which is one of the strengths of the Mechanics Dpt at LISN.

Contribution

This article has been a major breakthrough in understanding the modeling of boundary conditions for a water/air free surface, the most common fluids on Earth.

Impact

The Journal of Fluid Mechanics is one of the most renowned journal in the domain of fluid dynamics. The impact of this research went beyond the fluid mechanics community. The interest in proposing novel boundary conditions for the Navier-Stokes equations led to an invitation to speak at an international applied mathematics conference: Invited talk by L. Martin Witkowski in a colloquium of EQUADIFF 15. Brno, Czech Republic, Jul. 11-15, 2022.