Neural Downscaling for Complex Systems: from Large-scale to Small-scale by Neural Operator
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914730101178368 |
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| author | Lai, Pengyu Wang, Jing Wang, Rui Yang, Dewu Fei, Haoqi Xu, Hui |
| author_facet | Lai, Pengyu Wang, Jing Wang, Rui Yang, Dewu Fei, Haoqi Xu, Hui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13016 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neural Downscaling for Complex Systems: from Large-scale to Small-scale by Neural Operator Lai, Pengyu Wang, Jing Wang, Rui Yang, Dewu Fei, Haoqi Xu, Hui Computational Physics Adaptation and Self-Organizing Systems Fluid Dynamics 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. |
| title | Neural Downscaling for Complex Systems: from Large-scale to Small-scale by Neural Operator |
| topic | Computational Physics Adaptation and Self-Organizing Systems Fluid Dynamics |
| url | https://arxiv.org/abs/2403.13016 |