2026-10-27 · ArXiv
arXiv:2607.25790v2 Announce Type: replace-cross
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, is incorporated into the training objective to promote physically consistent and generalizable predictions. Numerical experiments on three EBB vibration problems demonstrate the effectiveness of the proposed framework. Comparisons with strong baseline models 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 an average reduction of approximately 79% in the mean relative $\mathcal{L}_2$ error compared with the best-performing baseline across the three benchmark problems. These results demonstrate the effectiveness of SpectONet as an accurate physics-guided operator-learning framework for structural vibration analysis.
原文链接：https://arxiv.org/abs/2607.25790
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