复杂系统的神经降尺度:从大规模到小规模的神经运算器

Pengyu Lai, Jing Wang, Rui Wang, Dewu Yang, Haoqi Fei, Hui Xu
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引用次数: 0

摘要

预测和理解复杂系统中的混沌动力学在各种应用中至关重要。然而,传统方法,无论是全尺度模拟还是忽略小尺度,都无法提供全面的解决方案。在本文中,我们介绍了一种名为神经降尺度(ND)的新方法,它将神经算子技术与惯性manifold 和非线性 Galerkin 理论相结合。ND 可有效地从在低维空间中得到良好体现的相应大尺度动力学推导出互补子空间中的小尺度动力学。在 Kuramoto-Sivashinsky 和 Navier-Stokes 方程所支配的复杂系统中,证明了该方法的有效性和通用性。作为第一个针对小尺度动力学的综合确定性模型,ND 揭示了复杂系统错综复杂的时空非线性动力学,揭示了小尺度动力学如何与大尺度动力学错综复杂地联系在一起并受其影响。
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Neural Downscaling for Complex Systems: from Large-scale to Small-scale by Neural Operator
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.
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