Generative Learning for Forecasting the Dynamics of Complex Systems
Han Gao Sebastian Kaltenbach Petros Koumoutsakos
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. The results
demonstrate that generative learning offers new frontiers for the accurate
forecasting of the statistical properties of complex systems at a reduced
computational cost.