Adaptive SIREN-PINN With Principled Initialization: A Frequency-Aware and Singularity-Robust Framework for Solver-Free Acoustic Seismic Wave Modeling

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving acoustic seismic wave equations in geophysical modeling. However, they often encounter challenges such as spectral bias, gradient instability, and slow convergence when applied to complex media, high-frequency wavefields, and singular source terms. To address these limitations, we propose Adaptive SIREN-PINNs, an enhanced framework that integrates learnable amplitude and frequency modulation parameters into the Sinusoidal Representation Networks (SIRENs), which employs periodic activation functions to naturally represent continuous signals and their derivatives, along with a principled weight initialization strategy. This enhancement improves the model’s frequency-aware representation capability, enabling it to better capture both low- and high-frequency components while enhancing gradient propagation stability during training. Furthermore, to mitigate the singularity associated with point sources, we adopt a Gaussian approximation of the Dirac function and reformulate the wave equation in terms of the scattered wavefield, following established regularization practices in seismic wave modeling. Additionally, we conduct a spectral analysis of the Neural Tangent Kernel (NTK) to gain insights into the model’s learning dynamics across different frequency components during training. Numerical experiments conducted on isotropic homogeneous medium, the Marmousi model, and anisotropic TTI/VTI medium demonstrate that the proposed method significantly outperforms conventional PINNs and baseline SIREN-PINNs in terms of wavefield reconstruction accuracy and convergence efficiency. The results validate the effectiveness of the adaptive SIREN mechanism in improving both the expressive power and training stability of PINNs, offering a mesh-free and solver-free alternative to traditional numerical methods.