Gabor-Enhanced Physics-Informed Neural Networks for Fast Simulations of Acoustic Wavefields

2025-02-24

AI Summary

To address the low-frequency bias inherent in physics-informed neural networks (PINNs) when solving the Helmholtz equation—leading to poor accuracy and slow convergence in high-frequency acoustic wavefield modeling—this paper proposes a Gabor-embedded simplified PINN framework. The method directly maps spatial coordinates into a custom-designed Gabor basis space, explicitly encoding the oscillatory and localized nature of wavefields. We introduce, for the first time, an auxiliary-network-free Gabor coordinate embedding mechanism and efficiently incorporate perfectly matched layer (PML) absorbing boundary conditions into the PINN formulation. Experiments on the Marmousi and Overthrust benchmark velocity models demonstrate that our approach achieves over 40% faster convergence and reduces relative error by approximately 55% compared to standard PINNs and earlier Gabor-PINN variants, while significantly improving training stability.

Technology Category

• Machine Learning: Hardware-aware ML
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Enhances high-frequency wavefield simulation accuracy
• Simplifies Gabor function integration in neural networks
• Improves convergence speed and robustness in seismic modeling

Innovation

• Gabor-enhanced PINNs
• Custom Gabor coordinate mapping
• Integrated PML for boundaries