Generative Learning for Forecasting the Dynamics of Complex Systems

Understand

We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics.

• In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are down sampled to a lower dimensional manifold that is evolved through an auto-regressive attention mechanism.
• In turn, Bayesian diffusion models, that map this low-dimensional manifold onto its corresponding high-dimensional space, capture the statistics of the system dynamics.
• We demonstrate the capabilities and drawbacks of G-LED in simulations of several benchmark systems, including the Kuramoto-Sivashinsky (KS) equation, two-dimensional high Reynolds number flow over a backward-facing step, and simulations of three-dimensional turbulent channel flow.