Kavli Affiliate: Jing Wang
| First 5 Authors: Jing Wang, Zheng Li, Pengyu Lai, Rui Wang, Di Yang
| Summary:
Multiscale phenomena manifest across various scientific domains, presenting a
ubiquitous challenge in accurately and effectively simulating multiscale
dynamics in complex systems. In this paper, a novel decoupling solving mode is
proposed through modelling large-scale dynamics independently and treating
small-scale dynamics as a slaved system. A Spectral Physics-informed Neural
Network (PINN) is developed to characterize the small-scale system in an
efficient and accurate way. The effectiveness of the method is demonstrated
through extensive numerical experiments, including one-dimensional
Kuramot-Sivashinsky equation, two- and three-dimensional Navier-Stokes
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 paper presents a valuable
and promising approach to enhance the computational simulations of multiscale
spatiotemporal systems, which enables the acquisition of large-scale data with
minimal computational demands, followed by Spectral PINN to capture small-scale
dynamics with improved efficiency and accuracy.
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