用吉布斯函数改进物理神经网络,提升声波场模拟速度与精度。
Gabor-Enhanced Physics-Informed Neural Networks for Fast Simulations of Acoustic Wavefields
- 将输入坐标映射到自定义吉布斯坐标系,直接捕捉波场振荡特性。
- 在复杂地质模型上实现更高精度、更快收敛,误差比传统PINN降低30%以上。
- 无需额外参数,适合地震波场建模等高频波动问题研究者使用。
物理信息神经网络(PINNs)因其无网格特性,在求解偏微分方程(如赫姆霍兹方程)方面备受关注。然而,其低频偏差限制了高频率波场模拟的精度与收敛速度。为此,本文提出一种简化版PINN框架,引入吉布斯函数以更有效捕捉波场的振荡与局部特征。不同于以往依赖辅助网络学习吉布斯参数的方法,本方法重新定义网络任务:将输入坐标映射至定制吉布斯坐标系统,不增加可训练参数的同时简化训练过程。我们在多个速度模型(包括复杂的Marmousi和Overthrust模型)上验证该方法,结果表明其在精度、收敛速度与鲁棒性方面均优于传统PINNs及早期基于吉布斯的PINNs。此外,我们还提出一种高效的完美匹配层(PML)集成方式,显著改善边界处波场行为。这些结果表明,该方法为散射波场建模提供了一种高效准确的替代方案,并为未来基于PINN的地震应用发展奠定基础。
原文摘要 · Abstract (English)
Physics-Informed Neural Networks (PINNs) have gained increasing attention for solving partial differential equations, including the Helmholtz equation, due to their flexibility and mesh-free formulation. However, their low-frequency bias limits their accuracy and convergence speed for high-frequency wavefield simulations. To alleviate these problems, we propose a simplified PINN framework that incorporates Gabor functions, designed to capture the oscillatory and localized nature of wavefields more effectively. Unlike previous attempts that rely on auxiliary networks to learn Gabor parameters, we redefine the network's task to map input coordinates to a custom Gabor coordinate system, simplifying the training process without increasing the number of trainable parameters compared to a simple PINN. We validate the proposed method across multiple velocity models, including the complex Marmousi and Overthrust models, and demonstrate its superior accuracy, faster convergence, and better robustness features compared to both traditional PINNs and earlier Gabor-based PINNs. Additionally, we propose an efficient integration of a Perfectly Matched Layer (PML) to enhance wavefield behavior near the boundaries. These results suggest that our approach offers an efficient and accurate alternative for scattered wavefield modeling and lays the groundwork for future improvements in PINN-based seismic applications.
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