Learning periodic shear flow dynamics via physically aligned generative flow model

Abstract

The modeling of complex spatiotemporal dynamics has been extensively investigated across diverse physical systems due to its critical role in understanding and predicting time-dependent physical behavior. While several previous studies have shown promising results in addressing the inherent limitations of transient modeling, significant challenges remain in accurately predicting condition-dependent state transitions and controlling accumulated errors. In this study, we propose a deep learning approach for efficient and stable modeling of complex spatiotemporal dynamics. Specifically, the proposed framework aligns the generative process of flow matching with physical temporal evolution, thereby enabling direct modeling of state transitions. Both quantitative and qualitative evaluations demonstrate that the proposed model achieves superior generative performance, showing improvements of up to 86% in variance-scaled root mean squared error and 46% in structural similarity index measure compared to baseline models. Moreover, we highlight the computational advantage of the proposed framework, achieving high predictive performance while requiring 8–49 times less inference time than the baseline models. The proposed approach not only enables accurate and stable long-horizon generation but also provides a promising framework for efficient modeling of complex spatiotemporal dynamics.