AI 中文总结
本文提出ModalONet，利用DeepONet分支-主干分解特性，仅从动力系统响应场恢复模态基，在四类结构系统上实现高精度模态识别，验证了神经算子用于模态识别的潜力。
AI 中文摘要
DeepONet（深度算子网络）、LNO（拉普拉斯神经算子）等神经算子是有效的替代模型，但它们几乎仅被训练用于复现系统的正向响应，而非其固有结构，比如结构系统的模态特性。本文提出ModalONet，将算子学习用于不同场景：无需特征求解器和带标签的模态，直接从动力系统的响应场中恢复其模态基，即振型、固有频率和阻尼比。核心发现是DeepONet的分支-主干分解本身是一种可学习的模态叠加形式：主干提供连续、无网格的振型，LNO分支提供极点-留数形式的模态坐标，每个学习到的极点对应一个固有频率和阻尼比。训练仅使用响应场，采用由重构、正交性和时间投影一致性组成的复合损失函数。对于简支和悬臂欧拉-伯努利梁、矩形和（退化）方形基尔霍夫板这四个结构系统，ModalONet恢复的解析模态基，每个振型的模态保证准则（MAC）值至少为0.998，固有频率误差在5%以内，阻尼比误差在7%以内，证明神经算子作为准确且可解释的模态识别工具具有潜力。
英文摘要
Neural operators such as the deep operator network (DeepONet) and the Laplace neural operator (LNO) are effective surrogates, but they are almost exclusively trained to reproduce the forward response of a system rather than its intrinsic structure, such as the modal properties of a structural system. We introduce ModalONet, which puts operator learning to a different use, such as recovering the modal basis, namely: mode shapes, natural frequencies, and damping ratios of a dynamical system directly from its response field, with no eigensolver and no labeled modes. Our key observation is that the DeepONet branch-trunk factorization is itself a learnable form of modal superposition: the trunk supplies continuous, mesh-free mode shapes, while an LNO branch supplies the modal coordinates in pole-residue form, so that each learned pole yields a natural frequency and a damping ratio. Training uses the response field alone, under a composite loss of reconstruction, orthonormality, and temporal projection consistency. The degenerate (equal-frequency) modes are resolved by a separable trunk and a shared frequency parameter, with post-hoc log-envelope regression improves the damping ratio estimates. Across four structural systems, namely: simply supported and cantilever Euler-Bernoulli beams and rectangular and (degenerate) square Kirchhoff plates, the ModalONet recovers the analytical modal basis with modal assurance criterion (MAC) values of at least 0.998 for every mode shape, natural frequency errors within 5%, and damping ratio errors within 7%, demonstrating the potential of neural operators as accurate and interpretable tools for modal identification.
