Machine Learning of turbulence models in Computational Fluid Dynamics

When:
15/05/2021 – 16/05/2021 all-day
2021-05-15T02:00:00+02:00
2021-05-16T02:00:00+02:00

Offre en lien avec l’Action/le Réseau : – — –/– — –

Laboratoire/Entreprise : Sorbonne Center for Artificial Intelligence – Sorb
Durée : 36 mois
Contact : patrick.gallinari@sorbonne-universite.fr
Date limite de publication : 2021-05-15

Contexte :
Numerical simulation of fluids plays an essential role in modeling complex physical phenomena in domains ranging from climate to aerodynamics. Fluid flows are well described by Navier-Stokes equations, but solving these equations at all scales remains extremely complex in many situations and only an averaged solution supplemented by a turbulence model is simulated in practice. Unfortunately turbulence models present important weaknesses (Xiao and Cinnella, 2019). The increased availability of large amounts of high fidelity data and the recent development and deployment of powerful machine learning methods has motivated a surge of recent work for using machine learning in the context of computational fluid dynamics (CFD), and specifically turbulence modelling (Durasaimy et al., 2019). Combining powerful statistical techniques and model-based methods leads to an entirely new perspective for CFD. From the machine learning (ML) side, modeling complex dynamical systems and combining model-based and data-based approaches is the topic of active new research directions. This is then the context of this project, and our aim is to develop the interplay between Deep Learning (DL) and CFD in order to improve turbulence modeling and to challenge state of the art ML techniques.

Sujet :
Objective: Combining CFD models and Deep Learning

Our objective is to improve traditional CFD models, both in terms of complexity and of accuracy of the predictions, with the addition of ML components. Recent progresses, and the generalized use of automatic differentiation both for differentiable solvers and DL algorithms have paved the road to the integration of DL techniques and ODE/PDE solvers. In the ML community, a starting point for such investigations was the Neural ODE paper (Chen 2018) that promoted the use of ODE solvers for ML problems. We advocate for this research the use of DL modules for complementing CFD solvers, in the spirit of (Le Guen 2021) who introduced a principled approach however still limited to basic PDEs. In our new context, we will analyze how to model unclosed terms in the Reynolds-Averaged Navier-Stokes (RANS) equations. This approach can be seen as a generalization of classical closure models. In order to make easier this theoretical analysis, the approach will be first developed for a scalar surrogate of the Navier-Stokes equations, namely, the nonlinear Burgers’ equation, which has been widely used in the literature as a simplified ansatz for Navier-Stokes turbulence. The framework will then be deployed and adapted to the specificity of unsteady RANS simulations. Turbulence model agmentation will be achieved by supplementing classical closure models for which we have prior knowledge with data-driven corrections. The whole system will be trained end to end with the DL modules and the numerical solvers using high-fidelity data.
In order to be useful for CFD applications a learned model must accurately simulate flows outside of the training distribution: operational conditions and environment may vary according to different physical factors thus requiring models to extrapolate to these new conditions. DL could in principle be extremely efficient for learning complex dynamics but they struggle with generalization to out-of-distribution data. We will adopt a new perspective by considering learning dynamical models from multiple environments and propose a new framework leveraging the commonalities and discrepancies among environments. We expect this new setting to be more robust to new distributions than classical empirical risk minimization or robust optimization schemes.

References

Xiao H., Cinnella P. 2019, Quantification of model uncertainty in RANS simulations: A review. Progress in Aerospace Sciences, 108 (2019), 1-31.
Duraisamy K., Iaccarino G., and Xiao H., Turbulence modeling in the age of data, Annual Review of Fluid Mechanics 51, 357 (2019).
Chen, R.T.Q. et al., 2018. Neural Ordinary Differential Equations. NIPS (2018), 31–60.
Le Guen V., Yin Y., Dona J., Ayed I., de Bézenac E., Thome N., Gallinari, P. 2021. Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting. ICLR (2021), 1–22.
Schmelzer M., Dwight R.P., Cinnella P. 2020, Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression. Flow, Turbulence and Combustion 104 (2020), 579–603.
Gautier N. et al., 2015 Closed-loop separation control using machine learning. Journal of Fluid Mechanics, 770 (2015), 442–457
Arjovsky M. et al. 2020. Invariant Risk Minimization. arxiv.org/abs/2002.04692 (2020), 1–31.
Bhattacharya K. et al. 2020, Model reduction and neural networks for para- metric pdes. Preprint arXiv:2005.03180 (2020).
Kochkov, D. et al. 2021. Machine learning accelerated computational fluid dynamics. (2021), 1–13.
Um K. et al. 2020. Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers. Neurips (2020), 1–12.
Sirignano J., MacArt J.F., Freund J.B. 2020. DPM: A deep learning PDE augmentation method with application to large-eddy simulation. Journal of Computational Physics. 423, (2020), 109811.
Wang R. et al. 2020, Towards physics-informed deep learning for tur- bulent flow prediction, in Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Dis- covery & Data Mining (2020), 1457–1466.
Willard J.D. et al. 2020. Integrating physics-based modeling with machine learning: A survey. arXiv (2020), 1–34.

Profil du candidat :
Master of science in engineering, computer science or applied mathematics

please send the following information to P. Cinnella and P. Gallinari. CV, motivation letter, grades obtained in master, recommandation letters when possible.

Formation et compétences requises :
Good background in mathematics applied to fluid mechanics, in computer science and in machine learning

Adresse d’emploi :
Sorbonne Université, 75005 Paris
SCAI – Sorbonne Center for AI –
The applicant will work jointly at Institut Jean le Rond d’Alembert (Fluid Mechanics) and at LIP6 (Computer Science)