Physics-Informed Data-Driven Tools: From Ideal models to Geophysical systems

Abstract: Our ability to collect data is rapidly increasing thanks to computational power and the unprecedented diversity of sensors. But how good are we at extracting, reconstructing, and understanding information from them? Big data are not easy to digest. Our knowledge about the Earth system is not increasing at the same speed as data, but it follows the slower progress of Data Reconstruction and Modelling techniques. Performing in-silico experiments on ideal/complex systems, we examine the applicability of Physics-Informed Data-Driven (PIDD) tools to extract interpretable information from sparse & heterogeneous observations of complex flows. Key applications are data-driven physics modeling, data augmentation, and super-resolution. We compare state-of-the-art purely Data-Driven tools, such as Generative Adversarial Networks (GAN) [1], with purely Physics-Informed approaches, such as Nudging [2], on the ability to reconstruct missing data. At the same time, we will discuss how the potentials of both techniques are combined in the most advanced Physics-Informed Neural Networks. Moving from ideal cases such as turbulence on a rotating frame or Rayleigh-Benard convection I will discuss how PIDD tools can potentially result in a ground-breaking methodological revolution of today's data analysis and data-reconstruction techniques in applications such as ocean observations [3,4].

[1] M. Buzzicotti, F. Bonaccorso, P. Clark Di Leoni, L. Biferale. Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot database. Physical Review Fluids 6 (5), 050503, (2021).
[2] M. Buzzicotti, P. Clark Di Leoni. Synchronizing subgrid scale models of turbulence to data. Physics of Fluids 32 (12), 125116, (2021).
[3] B.A. Storer, M. Buzzicotti, H. Khatri, S.M. Griffies, H. Aluie. Global energy spectrum of the general oceanic circulation. Nature communications 13 (1), 1-9, (2022).
[4] M. Buzzicotti, B.A. Storer, S.M. Griffies, H. Aluie. A coarse-grained decomposition of surface geostrophic kinetic energy in the global ocean. Earth and Space Science Open Archive: ESSOAr & arXiv preprint arXiv:2106.04157, (2021).

Bio: Michele Buzzicotti is a theoretical physicist at the University of Rome Tor Vergata active in the field of Statistical Mechanics and Complex Systems. His main research activity is in the study of turbulent flows using Direct Numerical Simulations and Artificial Intelligence. Working from both Eulerian and Lagrangian points of view, he is interested in the development of new paradigms for data analysis as well as of non-linear, out of equilibrium models, such as Large-Eddy-Simulation closures for the small-scale dynamics of high Reynolds flows.
Michele Buzzicotti is part of the ERC Advanced Grant project "Smart-TURB", PI: Prof. Luca Biferale. At the same time, he has recently started a collaboration with Prof. Hussein Aluie from the the University of Rochester (NY, USA) on the data dnalysis of Geophysical flows where the main goal is to disentangle the role of the multiscale physics at play in the Ocean.