发表机构
Department of Mathematics and Scientific Computing, National Institute of Technology Hamirpur; The Hatter Department of Marine Technologies, Leon H. Charney School of Marine Sciences, University of Haifa（印度国家技术学院哈米尔布尔分校数学与科学计算系; 海法大学莱昂·H·查尔尼海洋科学学院哈特海洋技术系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对欧拉 - 伯努利梁振动问题，提出SpectONet框架，融合DeepONet算子学习能力、物理信息约束与CGL传感器放置，采用非均匀谱传感器位置，经实验验证其比多个基线模型预测误差更低，为结构振动分析提供有效框架。
AI 中文摘要
本文提出了一种名为SpectONet的新型物理引导谱深度算子网络，用于解决欧拉 - 伯努利梁（EBB）振动问题。该框架将DeepONet的算子学习能力与物理信息约束及切比雪夫 - 高斯 - 洛巴托（CGL）传感器放置相结合。与传统DeepONet框架不同，SpectONet使用非均匀谱传感器位置，在域边界附近点更密集。这一采样策略改善了边界敏感结构响应的有限维表示。将控制梁方程及相关初始和边界条件纳入训练目标，以促进物理上一致且可推广的预测。通过数值实验验证了其有效性，与多个基线模型比较，SpectONet在所有评估指标上预测误差更低，在三个合成问题上比基线模型至少提高64%，在实际问题上至少提高37%。结果表明SpectONet为结构振动分析提供了准确、计算高效且物理一致的算子学习框架。
英文摘要
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.
