Generative Learning for Forecasting the Dynamics of Complex Systems
This work addresses computational bottlenecks in simulating complex systems like fluid dynamics, offering a method for faster forecasting, though it appears incremental as it builds on existing generative and attention-based techniques.
The authors tackled the problem of accelerating simulations of complex systems by introducing G-LED, a generative model that reduces computational cost while forecasting statistical properties, achieving accurate results in benchmark systems like turbulent flows.
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.