Generative Learning for Forecasting the Dynamics of Complex Systems
<|reference_start|>Generative Learning for Forecasting the Dynamics of Complex Systems: 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.<|reference_end|>
@article{gao2024generative,
    title={Generative Learning for Forecasting the Dynamics of Complex Systems},
    author={Han Gao, Sebastian Kaltenbach, Petros Koumoutsakos},
    journal={arXiv preprint arXiv:2402.17157},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.17157},
    primaryClass={cs.LG physics.comp-ph physics.flu-dyn stat.ML}
}