中国物理B ›› 2025, Vol. 34 ›› Issue (3): 34702-034702.doi: 10.1088/1674-1056/ada7dc

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Learning complex nonlinear physical systems using wavelet neural operators

Yanan Guo(郭亚楠)1,2,3, Xiaoqun Cao(曹小群)1,†, Hongze Leng(冷洪泽)1, and Junqiang Song(宋君强)1   

  1. 1 College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China;
    2 College of Computer, National University of Defense Technology, Changsha 410073, China;
    3 Naval Aviation University, Huludao 125001, China
  • 收稿日期:2024-12-01 修回日期:2025-01-02 接受日期:2025-01-09 发布日期:2025-03-15
  • 通讯作者: Xiaoqun Cao E-mail:caoxiaoqun@nudt.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 42005003 and 41475094).

Learning complex nonlinear physical systems using wavelet neural operators

Yanan Guo(郭亚楠)1,2,3, Xiaoqun Cao(曹小群)1,†, Hongze Leng(冷洪泽)1, and Junqiang Song(宋君强)1   

  1. 1 College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China;
    2 College of Computer, National University of Defense Technology, Changsha 410073, China;
    3 Naval Aviation University, Huludao 125001, China
  • Received:2024-12-01 Revised:2025-01-02 Accepted:2025-01-09 Published:2025-03-15
  • Contact: Xiaoqun Cao E-mail:caoxiaoqun@nudt.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 42005003 and 41475094).

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摘要： Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors. Numerical simulations play a pivotal role in nonlinear science, serving as a critical tool for revealing the underlying principles governing these systems. In addition, they play a crucial role in accelerating progress across various fields, such as climate modeling, weather forecasting, and fluid dynamics. However, their high computational cost limits their application in high-precision or long-duration simulations. In this study, we propose a novel data-driven approach for simulating complex physical systems, particularly turbulent phenomena. Specifically, we develop an efficient surrogate model based on the wavelet neural operator (WNO). Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs. In simulations of complex physical fields, the improved WNO model outperforms established deep learning models, such as U-Net, ResNet, and the Fourier neural operator (FNO), in terms of accuracy. Notably, the improved WNO model exhibits exceptional generalization capabilities, maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining. This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems, providing strong evidence to support the development of more efficient, scalable, and high-precision simulation techniques.

关键词: nonlinear science, turbulence, deep learning, wavelet neural operator

Abstract: Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors. Numerical simulations play a pivotal role in nonlinear science, serving as a critical tool for revealing the underlying principles governing these systems. In addition, they play a crucial role in accelerating progress across various fields, such as climate modeling, weather forecasting, and fluid dynamics. However, their high computational cost limits their application in high-precision or long-duration simulations. In this study, we propose a novel data-driven approach for simulating complex physical systems, particularly turbulent phenomena. Specifically, we develop an efficient surrogate model based on the wavelet neural operator (WNO). Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs. In simulations of complex physical fields, the improved WNO model outperforms established deep learning models, such as U-Net, ResNet, and the Fourier neural operator (FNO), in terms of accuracy. Notably, the improved WNO model exhibits exceptional generalization capabilities, maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining. This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems, providing strong evidence to support the development of more efficient, scalable, and high-precision simulation techniques.

Key words: nonlinear science, turbulence, deep learning, wavelet neural operator

中图分类号:  (Turbulence simulation and modeling)

  • 47.27.E-
02.60.Cb (Numerical simulation; solution of equations) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence) 02.30.Jr (Partial differential equations)