Least-squares-embedded optimization for accelerated convergence of PINNs in high-frequency acoustic wavefield simulations
Year: 2026
Type: article
Abstract: Physics-Informed Neural Networks (PINNs) have shown promise in solving partial differential equations (PDEs), including the frequency-domain Helmholtz equation. However, standard training of PINNs using gradient descent (GD) suffers from slow convergence and instability, particularly for high-frequency wavefields in seismic scales. For scattered acoustic wavefield simulation based on the Helmholtz equation, we derive a hybrid optimization framework by embedding a least-squares (LS) solver directly into the GD loss function. This approach enables optimal updates for the linear output layer and mitigates the spectral bias of neural networks, making it especially effective for high-frequency problems. We provide practical, tensor-based implementations for Helmholtz formulations with and without perfectly matched layers (PML). Numerical experiments on benchmark velocity models demonstrate that the proposed method achieves faster convergence, higher accuracy, improved stability, and greater robustness to hyperparameter selection compared to conventional PINN training. In particular, our results show that the LS-enhanced method converges rapidly even in cases where standard GD-based training fails. Since the LS solver operates on small matrices embedded within the loss, it introduces minimal computational overhead and remains scalable for large-scale wavefield simulations.
Source: Computers & Geosciences
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,010
Funders: Ministerio de Ciencia, Innovación y Universidades, European Commission, Eusko Jaurlaritza, Euskal Herriko Unibertsitatea, Basque Center for Applied Mathematics, Agencia Estatal de Investigación, Spanish National Plan for Scientific and Technical Research and Innovation, H2020 Marie Skłodowska-Curie Actions, HORIZON EUROPE Marie Sklodowska-Curie Actions
OpenAlex ID: W7138402184