arXiv:2502.00897cs.LGphysics.geo-ph2025-02被引 3

用元学习与低秩分解加速地震波场建模,支持多频适应。

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network

  • 通过奇异值分解降低网络参数量,结合频率嵌入超网络实现自适应建模。
  • 在复杂速度模型上收敛速度提升3倍以上,精度显著优于传统PINN方法。
  • 适合需要快速泛化到新频率的地震成像与数值模拟场景。

物理信息神经网络(PINN)在复杂速度模型中模拟多频波场时面临收敛慢、高频细节表达差及频率泛化能力不足等问题。为此,我们提出Meta-LRPINN框架,结合奇异值分解(SVD)的低秩参数化、元学习与频率嵌入超网络(FEH)。通过将隐层权重进行SVD分解,并设计FEH将输入频率映射至奇异值,实现高效且频率自适应的波场表示。元学习提供鲁棒初始化,提升优化稳定性并减少训练时间。此外,在元测试阶段引入自适应秩缩减与FEH剪枝,进一步提高效率。数值实验表明,该框架在不同速度模型的多频散射波场任务中,相比Meta-PINN和原始PINN,收敛速度更快、精度更高,且对分布外频率具有强泛化能力,展现出在可扩展、自适应地震波场建模中的潜力。

原文摘要 · Abstract (English)

Physics-informed neural networks (PINNs) face significant challenges in modeling multi-frequency wavefields in complex velocity models due to their slow convergence, difficulty in representing high-frequency details, and lack of generalization to varying frequencies and velocity scenarios. To address these issues, we propose Meta-LRPINN, a novel framework that combines low-rank parameterization using singular value decomposition (SVD) with meta-learning and frequency embedding. Specifically, we decompose the weights of PINN's hidden layers using SVD and introduce an innovative frequency embedding hypernetwork (FEH) that links input frequencies with the singular values, enabling efficient and frequency-adaptive wavefield representation. Meta-learning is employed to provide robust initialization, improving optimization stability and reducing training time. Additionally, we implement adaptive rank reduction and FEH pruning during the meta-testing phase to further enhance efficiency. Numerical experiments, which are presented on multi-frequency scattered wavefields for different velocity models, demonstrate that Meta-LRPINN achieves much fast convergence speed and much high accuracy compared to baseline methods such as Meta-PINN and vanilla PINN. Also, the proposed framework shows strong generalization to out-of-distribution frequencies while maintaining computational efficiency. These results highlight the potential of our Meta-LRPINN for scalable and adaptable seismic wavefield modeling.

地震建模PINN元学习低秩分解

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。