# Addressing turbulent convection experimental data challenges in PINNs with appropriate physical sampling

Soufiane Mrini, Anne Sergent, Francesca Chillà, Julien Salort, Didier Lucor

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Soufiane Mrini, Anne Sergent, Francesca Chillà, Julien Salort, Didier Lucor. Addressing turbulent convection experimental data challenges in PINNs with appropriate physical sampling. Joint event European Colloquium on Data-Driven Fluid Dynamics/2nd ERCOFTAC Workshop on Machine Learning for Fluid Dynamics, Apr 2025, London, United Kingdom. hal-04924450

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Submitted on 31 Jan 2025

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# Addressing turbulent convection experimental data challenges in PINNs with appropriate physical sampling

Soufiane Mrini¹,², Anne Sergent¹,², Francesca Chillà³, Julien Salort³, Didier Lucor¹

¹ LISN-CNRS, Université Paris-Saclay, Orsay, France, ² Sorbonne Université, Paris, France, ³ Lab. Phys. ENS Lyon, France

Corresponding author: Soufiane.Mrini@soufiane.mrini@lisn.fr

Numerical and experimental approaches are becoming more complementary approaches to address highly turbulent regimes thanks to improvements in computation resources. Nonetheless, experimental results, such as meshless 3D3C Particle Tracking Velocimetry, are often spatially sparse, somewhat discontinuous, subject to measurement noise and incomplete, while CFD simulations still require intensive resources to solve all the time scales. To address these issues, we employ Physics Informed Neural Networks (PINNs) [2], which provide a meshless way to enrich and complement experimental data [1]. In the case of turbulent convection, our framework allows 3D temperature discovery, denoising, and generating continuous field representations [3]. Departing from the idealized case of Eulerian training-reconstruction, we propose a spatio-temporal sampling framework to tailor our DNS database to closely resemble experimental measurements. This poses additional challenges to PINNs particularly on addressing spatial gaps, tracking loss and scarcity of experimental-type labels. An important question arises on the optimal choice of collocation points to help alleviating these constraints. Our analysis focuses on the impact of PDE collocation points density through parallel GPU computations. Additionally, we explore the effectiveness of smart adaptive spatial PDE sampling to mitigate information loss with respect to relevant turbulent quantities caused by inherently noisy and sparse data.

This work benefits from the French National Research Agency funding (ANR-22-CE30-0018-02). Calculations were performed using HPC resources from GENCI-IDRIS (Grant 2a0326).

<figure><img src="image_3.png" /><figcaption>Figure 1: 3D-Reconstruction of instantaneous turbulent convection field ($Ra = 2 \times 10^9$, $Pr = 4.4$) from experimental-like data at iso-budget of labels. $N_R$ is the total number of PDE collocation points. Iso-surfaces of temperature and velocity magnitude at the boundaries with the same ground truth colorbar.</figcaption></figure>

## References

[1] S. Cai, C. Gray, and G. E. Karniadakis. Physics-informed neural networks enhanced particle tracking velocimetry: An example for turbulent jet flow. *IEEE Transactions on Instrumentation and Measurement*, 2024.

[2] M. Raissi, P. Perdikaris, and G.E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. *J. Comput. Phys.*, 378:686–707, 2019.

[3] D. Lucor, A. Agrawal, and A. Sergent. Simple computational strategies for more effective physics-informed neural networks modeling of turbulent natural convection. *J. Comput. Phys.*, 456:111022, 2022.