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Job Record #19142
TitlePhD in AI-based modeling of unsteady flows
CategoryPhD Studentship
EmployerCNAM Paris
LocationFrance, Paris
InternationalYes, international applications are welcome
Closure DateMonday, July 01, 2024

The massive reliance on computational fluid dynamics (CFD) for research and engineering has led to the 

creation of massive and ever-growing fluid dynamics databases. These are significantly under-leveraged by 

historically low-dimensional approaches. The parallel with recent trends in AI, which point to learning 

techniques that improve by exploiting very large datasets using high-dimensional formulations, suggests that 

large gains can be made by overcoming these limitations. These alternative methods improve the extraction 

of essential and relevant information and significantly improve modeling approaches. Many data-driven fluid 

models have started to include a large number of local variables, meaning the road to higher dimensionality 

now lies with context-aware strategies, which can learn to automatically extract relevant information about 

the surrounding flow state and domain topology to refine their predictions. In this project, we explore the 

benefits and challenges provided by using context-aware learning techniques to extract predictive reduced-
order model (ROM)s.

In the context of flow simulations, ROMs represent approximate but cheap models of a physical phenomenon, 

allowing for fast prototyping and multiple queries. Model order reduction consists of restricting the search of 

a solution to a low-dimensional space spanned by a reduced-order basis. The latter is inferred from a set of 

precomputed high-fidelity solutions commonly using linear dimensionality reduction techniques, such as 

proper-orthogonal decomposition (i.e. principal component analysis), dynamic mode decomposition, etc. 

Despite important progress, most state-of-the-art ROMs fail to demonstrate robustness to uncertainties 

while remaining predictive when highly unsteady and turbulent systems are concerned. The main drawback in 

most reduction techniques is that reduced bases are learned using linear dimensionality reduction techniques 

and do not properly handle nonlinear problems which are commonplace in complex flow configurations. 

Recently, making use of recent advances in neural network architecture, nonlinear dimentionality reduction 

techniques have been infused in ROM community, using autoencoders and Convolutional (CNN) and Graph 
(GNN) neural networks.

However, novel approaches examine using mesh-free approaches, such as coordinate-based NNs to learn 

basis functions directly from the continuous vector field itself and not from its discretization while dynamics 

are modeled in a latent space. This hyper-reduction approach is discretization-independent and features 

lower memory consumption than prior discretization-dependent ROM approaches be they linear (PODs) or 

nonlinear (auto-encoders). In the same spirit, neural operators, which allow learning discretization-free 

representations, can be explored to build ROMs. These mesh-free methods will be explored in this project.


The candidate should have a MSc degree or equivalent in fluid mechanics or applied mathematics, with 

experience in scientific computing.


Programming experience and expertise in data-driven techniques will be considered very positively.


The position is offered for the duration of 36 months, between October 1st, 2024 and September 30th, 2027. 


The applicant should include a CV, and a motivation letter.



[1] Johannes Brandstetter, Daniel E. Worrall, and Max Welling. “Message Passing Neural PDE Solvers”. In: 

International Conference on Learning Representations. 2022. 

[2] Rizal Fathony, Anit Kumar Sahu, Devin Willmott, and J Zico Kolter. “Multiplicative filter 

networks”. In: International Conference on Learning Representations. 2021.

[3] Vincent Sitzmann, Julien Martel, Alexander Bergman, David Lindell, and Gordon Wetzstein. “Implicit neural 

repre- sentations with periodic activation functions”. In: Advances in Neural Information Processing Systems 

33 (2020), pp. 7462–7473.

[4] Peter Yichen Chen et al. “CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural 

Representations”. In: ICLR 2023. 2022. url:

[5] Zongyi Li et al. “Fourier Neural Operator for Parametric Partial Differential Equations”. In: ICLR. 2021.

[6] C. Scherding, G. Rigas, D. Sipp, P.J. Schmid, and T. Sayadi, Ronaalp: Reduced-order nonlinear 

approximation with active learning procedure, 2023.

[7] C. Scherding, G. Rigas, D. Sipp, P. J. Schmid, and T. Sayadi, Data-driven framework for input/output 

lookup tables reduction: Application to hypersonic flows in chemical nonequilibrium, Phys. Rev. Fluids, 8 

(2023), p.023201 [8] S. Kneer, T. Sayadi, D. Sipp, P. Schmid, and G. Rigas, Symmetry-aware autoencoders: s-

pca and s-nlpca, arXiv, (2021), p. 2111.02893v2
Contact Information:
Please mention the CFD Jobs Database, record #19142 when responding to this ad.
NameTaraneh Sayadi
Email ApplicationYes
Record Data:
Last Modified11:49:18, Thursday, May 02, 2024

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