Agenda

Speaker: Luca Biferale, University of Roma Tor Vergata

Abstract:

We introduce a stochastic generative framework for the reconstruction and augmentation of complex, multiscale signals arising in nonlinear dynamical systems. The approach builds on generative Diffusion Models, a class of probabilistic deep learning methods capable of learning high-dimensional data distributions beyond Gaussian approximations. We demonstrate applications to both two-dimensional fields and one-dimensional stochastic signals, including the temporal evolution of turbulent observables along Lagrangian particle trajectories and sea-surface fields derived from satellite imagery. The proposed methodology is benchmarked against Gaussian Process Regression using complementary statistical diagnostics and pointwise error metrics. Particular emphasis is placed on the faithful reproduction of non-Gaussian statistics, intermittency, extreme events, and scale-dependent correlations. We further present preliminary results on generalization capabilities, robustness to model collapse, and the intrinsic limitations of black-box generative approaches in physics-driven contexts. Finally, we discuss long-term perspectives on data-driven stochastic modeling for complex systems, outlining key methodological challenges and the transformative potential of generative AI for advancing the quantitative modeling  of chaotic and stochastic systems and related multiscale phenomena.