Learning complex nonlinear physical systems using wavelet neural operators

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.