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PhD Physics on Turbulent convection: numerical modelling and physics-enhanced machine learning, Orsay

Du 1 octobre 2023 au 1 octobre 2026

Lab. Interdisciplinaire des Sciences du Numérique, Université Paris-Saclay
Contacts : Anne Sergent et Didier Lucor

At very high Rayleigh numbers, a very intense heat transfer regime appears for which the triggering mechanisms are still poorly understood. Using HPC numerical simulations and physics-guided machine learning techniques, we seek to extract from data physical information bringing to light the multi-scale interactions between different turbulent flow structures.

The Rayleigh-Benard convection is established in a cavity under the effect of a temperature difference imposed on the horizontal walls, the bottom wall being heated. The resulting flow in the turbulent regime is a multi-structured and multi-scale phenomenon characterized by the superposition of small-scale plumes (heat vectors), a large-scale mean flow filling the cavity, boundary layers and turbulent fluctuations. 

For many years, we have been simulating this physical phenomenon by direct numerical simulation (DNS). The transition to massively parallel simulations now allows us to consider calculations at parameter levels close to experiments. However, these calculations are very heavy and even if the spatio-temporal description of the flow can be very fine, it is difficult to approach statistically all the scales of the flow, to store all the computed fields, or to easily replay the sequences. 

Despite progress made by careful comparison of experimental and numerical simulations studies, key differences remain in the amount and nature of the information provided by each community, making conjoint understanding difficult. For instance, experimental data is incomplete (probes time series, 2D fields sequences or images), but well converged and can reach high forcings. Numerical simulations are fully resolved in space, but reach lower turbulence level and for shorter durations. The tremendous potential capabilities of recent physics-informed deep learning (DL) techniques will help in seamlessly integrating the benefits of each approach into a new modeling and comprehension of turbulent physics. 

In this project, we will take advantage of both perceptrons or (graph) convolutional neural networks frameworks enhanced with physical constraints, in order to mitigate the risks and to speed up and robustify the training phase of the models. More specifically, objectives are to infer missing data from experiments, and alleviate the cost of expensive numerical simulations by reducing the storage cost. 

This work will be carried out within the framework of the ANR THERMAL project (2023-2026), and will benefit from a strong interaction with our colleagues Francesca Chillà and Julien Salort from LP-ENS Lyon.

The project seeks to take advantage of the capabilities of machine learning techniques to reduce the complexity of the data. These techniques will be deployed at the interface between numerical models andsolvers, and experimentally acquired data, not only to facilitate comparison, but also to access unmeasured/unquantifiable information in terms of variables or resolution finesse, and to guide physical exploration.

Two types of architecture will be considered based on deep or graph convolution neural networks, in which physical constraints enrich the output data for an accelerated convergence, with two distinct objectives. First, it is about processing multi-source experimental data acquisition to reconstruct hidden quantities fields, and test ideas about the super-resolution reconstruction to improve the spatial resolution of measures. Second, it is to extract physical informations from experimental images. DNS data are used for preliminary tests, but also provide additional information, leading to mixing of experimental and numerical databases.

Several encouraging internships have already been carried out on the topic [Lucor et al. JCP 2022]. A large DNS database already exists [Belkadi et al. JFM 2021], but it will be expanded as needed using the resources of GENCI’s national supercomputers. The project will focus on hidden scalar or field variables reconstruction and/or superresolution using DNS or / and experimental data, useful to better understand physical couplings between simultaneous flow quantities.