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Reconstructing Rayleigh–Bénard flows out of temperature-only measurements using Physics-Informed Neural Networks

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Abstract

We investigate the capabilities of Physics-Informed Neural Networks (PINNs) to reconstruct turbulent Rayleigh–Bénard flows using only temperature information. We perform a quantitative analysis of the quality of the reconstructions at various amounts of low-passed-filtered information and turbulent intensities. We compare our results with those obtained via nudging, a classical equation-informed data assimilation technique. At low Rayleigh numbers, PINNs are able to reconstruct with high precision, comparable to the one achieved with nudging. At high Rayleigh numbers, PINNs outperform nudging and are able to achieve satisfactory reconstruction of the velocity fields only when data for temperature is provided with high spatial and temporal density. When data becomes sparse, the PINNs performance worsens, not only in a point-to-point error sense but also, and contrary to nudging, in a statistical sense, as can be seen in the probability density functions and energy spectra.

Graphical abstract

Visualizations of temperature (top) and vertical velocity (bottom) for the flow with \(\textrm{Ra}_2\). The left column shows the reference data, the other three columns show the reconstructions obtained with \(\ell /\delta = 1\), 14 and 31. The locations of the measuring probes (corresponding to the case with \(\ell =14\delta \)) are marked with white dots on top of \(T^r\). All visualizations share the same colorbar

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This project has received partial funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No. 882340))

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Authors and Affiliations

  1. Departmento de Ingeniería, Universidad de San Andrés, Buenos Aires, Argentina

    Patricio Clark Di Leoni

  2. Department of Physics and INFN, University of Rome “Tor Vergata”, Rome, Italy

    Lokahith Agasthya, Michele Buzzicotti & Luca Biferale

  3. Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, 3400, Austria

    Lokahith Agasthya

Authors
  1. Patricio Clark Di Leoni
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  2. Lokahith Agasthya
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  3. Michele Buzzicotti
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  4. Luca Biferale
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Contributions

LA and PC conceived and carried out the numerical experiments and analyzed the results. All authors worked on develo** the main idea, discussed the results and contributed to the final manuscript.

Corresponding author

Correspondence to Patricio Clark Di Leoni.

Additional information

T.I.: Quantitative AI in Complex Fluids and Complex Flows: Challenges and Benchmarks. Guest editors: Luca Biferale, Michele Buzzicotti, Massimo Cencini.

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Clark Di Leoni, P., Agasthya, L., Buzzicotti, M. et al. Reconstructing Rayleigh–Bénard flows out of temperature-only measurements using Physics-Informed Neural Networks. Eur. Phys. J. E 46, 16 (2023). https://doi.org/10.1140/epje/s10189-023-00276-9

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