Frequency-Domain Physics-Informed Neural Networks for Modeling and Parameter Inversion of Wave-Induced Seabed Response

Modeling the dynamic response of saturated marine soils is crucial yet computationally challenging for traditional methods. Meanwhile, purely data-driven models suffer from sparse data and lack of physical interpretability. To overcome these limitations, this study proposes an intelligent engineering framework based on a frequency-domain physics-informed neural network (FD-PINN) for the forward simulation and inverse parameter identification of saturated seabed soils. Constrained directly by physical laws during the learning process, FD-PINN remains highly reliable even when training data is sparse. By formulating the governing equations in the frequency domain, it directly predicts complex-valued displacement and pore-pressure phasors. Multiscale Fourier feature mappings mitigate spectral bias and capture boundary layers and high-frequency effects. For inverse problems, a phase-sensitive lock-in extraction strategy transforms time-domain measurements into robust frequency-domain targets, enabling the accurate and noise-tolerant identification of poroelastic parameters with clear physical meaning (nondimensional storage parameter S and permeability parameter $\Gamma$). Numerical experiments show that FD-PINN substantially outperforms conventional time-domain PINN, achieving relative $L^2$ errors of ${10}^{-2}\sim {10}^{-3}$ for single- and multi-frequency excitations typical of wave-induced loadings. In particular, $\Gamma$ is consistently recovered with sub-percent relative error, while S can be reliably identified with multi-frequency data. The framework offers a data-efficient, noise-robust approach for high-fidelity modeling and robust parameter inversion, which is particularly valuable in offshore environments where high-quality data is scarce.