Learning Turbulent and Chaotic Dynamics via Data-Driven Probabilistic Models
Leonardo Zepeda-Núñez
Google Inc.
Google Research
Chaotic dynamics and turbulence are ubiquitous phenomena spanning a wide array of physical systems, including plasmas. In such systems, closely spaced initial conditions diverge rapidly, severely limiting long-term predictability. Furthermore, the complex multi-scale interactions characteristic of turbulence make accurate simulations computationally prohibitive, as all relevant scales must be sufficiently resolved. Consequently, data-driven approaches that bypass the need to simulate every scale have become highly attractive.
In this talk, we will explore novel data-driven approaches for learning chaotic and turbulent dynamics by leveraging emerging probabilistic machine learning methodologies. Specifically, we will focus on generative models designed to capture both transient regimes and invariant measures. These include conditional score-based diffusion models for the fast and accurate statistical computation of fluid flows, alongside measure-matching regularization techniques that enforce the correct long-term statistics of trajectories. By learning the underlying distributions directly, rather than relying solely on deterministic trajectory matching, these methods offer stable, sample-efficient, and robust alternatives for modeling complex systems.
We will provide the mathematical rationale behind these methodologies, discuss their implementation details, and showcase their performance on challenging 3D turbulent flows across diverse physical regimes and geometries. Finally, we will highlight how these probabilistic, data-driven tools can be integrated into broader multi-fidelity computational frameworks to advance reliable simulations in plasma physics and beyond.