AI 中文总结
该研究提出混合PINN框架，用于计算广义非均匀层状介质中SH波的频散关系，经测试验证其可独立训练复用，为相关频散分析提供了可复用计算模块。
AI 中文摘要
本研究提出了一种用于计算连续变化非均匀层状结构中剪切水平（SH）波频散关系的数学与计算框架。该方法将非均匀层的贡献从完整频散关系中分离出来，利用物理信息神经网络（PINN）学习该贡献，随后整合训练好的模型以确定完整频散关系。研究考察了离散问题的数学性质，包括有限差分系统的奇异性和层解的振荡行为，同时为PINN近似建立了泛化误差估计。该框架首先在地震学构型上进行测试，该构型由花岗岩半空间上方的非均匀砂岩层组成，其中剪切模量和密度的变化率相互独立，考虑指数型非均匀性。在特殊情况下，所提方法通过解析解进行验证；对于一般构型，当均匀子层数量增加时，Haskell矩阵方法显示出向PINN预测的连续变化频散关系收敛。参数研究进一步证实了与基础物理的一致性。该方法的一个重要特征是，非均匀层方程可独立训练并在多种场景中复用。为证明这一点，将同一训练好的网络与受完全不同物理定律支配的压电和压磁基底耦合，凸显了该PINN框架作为非均匀层状介质频散分析可复用计算模块的潜力。
英文摘要
This work presents a mathematical and computational framework for computing the dispersion relations of shear horizontal (SH) waves in continuously varying heterogeneous layered structures. The approach isolates the contribution of the heterogeneous layer from the complete dispersion relation, learns this contribution using a physics-informed neural network (PINN) and subsequently incorporates the trained model to determine the complete dispersion relation. The mathematical properties of the discretized problem are investigated, including the singularity of the finite-difference system and the oscillatory behavior of the layer solution, while a generalization-error estimate is established for the PINN approximation. The framework is first tested on a seismological configuration consisting of a heterogeneous sandstone layer over a granite half-space, where exponential heterogeneity is considered with independent variation rates in shear modulus and density. The proposed approach is validated against analytical solutions in special cases, while for general configurations the Haskell matrix method demonstrates convergence toward the continuously varying dispersion relation predicted by the PINN as the number of homogeneous sublayers increases. Parametric studies further confirm consistency with the underlying physics. An important feature of the method is that the heterogeneous-layer equation can be trained independently and reused in multiple settings. To demonstrate this, the same trained network is coupled with piezoelectric and piezomagnetic substrates governed by fundamentally different physical laws, highlighting the potential of the PINN framework as a reusable computational module for dispersion analysis in heterogeneous layered media.
