这篇论文提出了SpectONet，在梁振动问题上比传统DeepONet误差降低至少64%，物理一致性更好，值得研究结构动力学的朋友一看。
该论文提出SpectONet，融合DeepONet与物理约束和Chebyshev-Gauss-Lobatto非均匀传感器放置。相比传统DeepONet使用均匀传感器，SpectONet在边界附近集中采样，提升边界敏感结构响应的表示效率。在三个合成EBB振动问题和真实桥梁振动数据集上，SpectONet相比Vanilla DeepONet、PI-DeepONet、PINN、CNN-UNet等基线，预测误差降低至少64%（合成问题）和至少37%（实测问题）。该方法实现了准确、计算高效且物理一致的算子学习框架。
SpectONet: A Physics-Guided Spectral Deep Operator Network for Euler-Bernoulli Beam Dynamics
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.