Year: 2024
Type: preprint
Abstract: Predicting and understanding the chaotic dynamics in complex systems is essential in various applications. However, conventional approaches, whether full-scale simulations or small-scale omissions, fail to offer a comprehensive solution. This instigates exploration into whether modeling or omitting small-scale dynamics could benefit from the well-captured large-scale dynamics. In this paper, we introduce a novel methodology called Neural Downscaling (ND), which integrates neural operator techniques with the principles of inertial manifold and nonlinear Galerkin theory. ND effectively infers small-scale dynamics within a complementary subspace from corresponding large-scale dynamics well-represented in a low-dimensional space. The effectiveness and generalization of the method are demonstrated on the complex systems governed by the Kuramoto-Sivashinsky and Navier-Stokes equations. As the first comprehensive deterministic model targeting small-scale dynamics, ND sheds light on the intricate spatiotemporal nonlinear dynamics of complex systems, revealing how small-scale dynamics are intricately linked with and influenced by large-scale dynamics.
Source: arXiv (Cornell University)
Authors: Lai, Pengyu, Wang, Jing, Wang, Rui, Yang, Dewu, Fei, Haoqi, Xu, Hui
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4393064043