SpectONet provides an accurate, computationally efficient, and physically consistent operator-learning framework for structural vibration analysis and achieves at least 64% improvement over the considered baseline models across the three synthetic problems and at least 37% for the real-world problems.
Abstract
This paper proposes a novel physics-guided spectral deep operator network, termed SpectONet, for solving Euler-Bernoulli beam (EBB) vibration problems. The proposed framework integrates the operator-learning capability of DeepONet with physics-informed constraints and Chebyshev-Gauss-Lobatto (CGL) sensor placement. Unlike conventional DeepONet frameworks, which commonly employ uniformly distributed sensors, SpectONet uses nonuniform spectral sensor locations with a higher concentration of points near the domain boundaries. This sampling strategy improves the finite-dimensional representation of boundary-sensitive structural responses while requiring only a limited number of branch-network inputs. The governing beam equation, together with the associated initial and boundary conditions, incorporated into the training objective to promote physically consistent and generalizable predictions. Numerical experiments on three synthetic EBB vibration problems and a real-world bridge vibration dataset demonstrate the effectiveness of the proposed framework. Comparisons with strong baselines such as, Vanilla DeepONet, PI-DeepONet, PINN, and CNN-UNet show that SpectONet consistently achieves lower prediction errors across all considered evaluation metrics. In particular, SpectONet achieves at least \(64\%\) improvement over the considered baseline models across the three synthetic problems and at least \(37\%\) for the real-world problems. These results demonstrate that SpectONet provides an accurate, computationally efficient, and physically consistent operator-learning framework for structural vibration analysis.
The results demonstrate that PINN achieves more accurate and stable full-field vibration reconstructions than conventional PINNs, particularly under conditions involving high-frequency modes, and highlights the potential of hybrid data-physics neural frameworks as an efficient and reliable approach for solving complex PDE-governed dynamical systems.
Hailong Liu, S. Hedayatrasa, Yunpeng Zhu et al.· e-Journal of Nondestructive...· 0 citations
Physics-Informed Neural Networks (PINNs) continue to suffer from limited training efficiency in predicting electromagnetic scattering from three-dimensional (3D) targets, resulting in particularly high retraining costs when target geometries or incident fields vary. To address this issue, we propose a transferable PINN framework constrained by discrete Maxwell operators. By embedding finite-difference electromagnetic operators into the loss function, the predicted fields directly satisfy the discrete Maxwell’s equations on the computational grid, thereby enhancing physical consistency and improving training stability. Furthermore, a layer-freezing strategy is employed to preserve the generalized wave priors learned from the source scenario. Consequently, training under novel geometries or incident conditions no longer relies on full-network retraining; instead, rapid prediction is achieved by fine-tuning a minimal set of task-specific parameters. Numerical results demonstrate that the proposed method significantly reduces the number of iterations and retraining costs while maintaining prediction accuracy, making it an effective tool for rapid electromagnetic simulations and optical device design.
The proposed SCV-PINN provides a robust and generalized extension of standard PINNs for complex-valued, multiscale, oscillatory, high-dimensional, and real-valued nonlinear PDEs.
Biswanath Barman, Rajendra K. Ray, Debdeep Chatterjee· 0 citations
We present a method for predicting the ocean acoustic pressure field from partially observed pressure magnitudes across range–depth locations. Our framework leverages a physics-informed graph neural network (PIGNN), in which graph connectivity encodes the local spatial structure of the waveguide and enables stable learning of highly oscillatory fields. The PIGNN is trained to map range and depth coordinates to complex acoustic pressure while enforcing the partial differential equation (PDE) governing underwater sound propagation. In large-scale environments, pressure fields often exhibit rapid phase fluctuations over kilometer-scale distances, even at frequencies below 100 Hz, leading to highly complex solution landscapes that standard neural networks struggle to approximate. A key contribution of this work is demonstrating that graph-based message passing, combined with the envelope function derived from the parabolic equation (PE) model, effectively mitigates this challenge by capturing local phase relationships and yielding a substantially smoother learning target. By jointly incorporating the governing PDE and the spatial structure of the environment, the PIGNN achieves accurate pressure predictions with limited training data and improved generalization. [Work supported by ONR (Code 322).]
J. Castro-Correa, Mohsen Badiey· Journal of the Acoustical So...· 0 citations
The results demonstrate that the proposed PRCT-Net substantially enhances computational efficiency while maintaining high prediction accuracy for two-phase flow problems, and supports single-stage training and sustained deployment, enabling robust inference across a wide range of unseen operating conditions.
Xiao Zhang, Qingkai Zhao, Xinyao Zeng et al.· Journal of Fluids Engineerin...· 0 citations