Multiscale phenomena manifest across various scientific domains, presenting a ubiquitous challenge in accurately and effectively predicting multiscale dynamics in complex systems. In this paper, a novel solving mode is proposed for characterizing multiscale dynamics through a decoupling method. By modelling large-scale dynamics independently and treating small-scale dynamics as a slaved system, a Spectral PINN is developed to approach the small-scale system in an orthogonal basis functional space. The effectiveness of the method is demonstrated through extensive numerical experiments, including one-dimensional Kuramot-Sivashinsky (KS) equation, two- and three-dimensional Navier-Stokes (NS) equations, showcasing its versatility in addressing problems of fluid dynamics. Furthermore, we also delve into the application of the proposed approach to more complex problems, including non-uniform meshes, complex geometries, large-scale data with noise, and high-dimensional small-scale dynamics. The discussions about these scenarios contribute to a comprehensive understanding of the method's capabilities and limitations. This novel decoupling approach simplifies the analysis and prediction of spatiotemporal systems, where large-scale data can be obtained with low computational demands, followed by Spectral PINNs for capturing small-scale dynamics with improved efficiency and accuracy.

翻译：多尺度现象广泛存在于各类科学领域中，对复杂系统中多尺度动力学的准确高效预测构成了普遍性挑战。本文提出了一种新型求解模式，通过解耦方法表征多尺度动力学。通过独立建模大尺度动力学并将小尺度动力学视为受控系统，本研究开发了谱PINN，在正交基函数空间中逼近小尺度系统。通过包含一维Kuramot-Sivashinsky（KS）方程、二维及三维Navier-Stokes（NS）方程在内的大量数值实验验证了该方法有效性，展示了其在流体动力学问题处理中的通用性。此外，我们还深入探讨了该方法在非均匀网格、复杂几何构型、含噪大尺度数据以及高维小尺度动力学等更复杂问题中的应用。这些场景的讨论有助于全面理解该方法的优势与局限性。这种新型解耦方法简化了时空系统的分析与预测，可在低计算需求下获取大尺度数据，继而通过谱PINN以更高效率与精度捕获小尺度动力学。