Solving Acoustic Wave Equation with Koopman Neural Operator

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ID: 314587
2026
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Abstract
Summary Solving wave equations using machine learning methods, such as physics-informed neural networks (PINNs) and neural operator approaches, has become an active area of research in the computational seismology community. However, a significant challenge associated with these methods is the degradation of long-term prediction accuracy, which arises from the inherently nonlinear dynamics of wavefields governed by partial differential equations (PDEs). Koopman theory provides a promising framework by enabling the transformation of nonlinear dynamical systems into linear ones, thus allowing linear analysis tools to be applied to complex, nonlinear problems. In this study, we introduce a data-driven operator learning method, the Koopman Neural Operator (KNO), for solving the two-dimensional acoustic wave equation in the time domain. Within the KNO framework, the time-domain wavefield is treated as the state variables, while the velocity model acts as the control variables. These form a nonlinear dynamical system, which is mapped into a linear latent space using a convolutional encoder. The Koopman operator is then approximated by parameterizing the integral kernel in the wavenumber domain, facilitating linear time evolution of the encoded variables. A convolutional decoder subsequently transforms the evolved latent variables back into the original wavefield domain to obtain the predicted time-domain wavefields. To evaluate the performance of KNO, we first conducted numerical experiments on the three most complex datasets from the OpenFWI benchmark and compared the results with those of the current state-of-the-art Fourier Neural Operator (FNO). The results demonstrate that KNO outperforms FNO in terms of prediction accuracy, computational efficiency, memory consumption, and convergence speed. Additionally, KNO exhibits notably strong stability in seismic wavefield extrapolation on the Marmousi model. Finally, we comprehensively evaluate the parallel scalability of the proposed KNO model, and compared KNO with the finite difference method (FDM) (based on both CPU and GPU) in terms of computational speed. Collectively, these experiments indicate that KNO provides a promising new approach for long-term and relatively high-precision wavefield extrapolation in seismic modeling.
Reference Key
openalex_W7162010489 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Rongqi Bi, Peng Yong, Jianping Huang, Zixiao Zhang
Journal geophysical journal international
Year 2026
DOI
10.1093/gji/ggag196
URL
https://doi.org/10.1093/gji/ggag196
Keywords Keywords not found

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