Realtime finite element modeling of bridges assists modern structural health monitoring systems by providing comprehensive insights into structural integrity. This capability is essential for ensuring the safe operation of bridges and preventing sudden catastrophic failures. However, FEM computational cost and the need for realtime analysis pose significant challenges. Additionally, the input data is a 7 dimensional vector, while the output is a 1017 dimensional vector, making accurate and efficient analysis particularly difficult. In this study, we propose a novel hybrid quantum classical Multilayer Perceptron pipeline leveraging Symmetric Positive Definite matrices and Riemannian manifolds for effective data representation. To maintain the integrity of the qubit structure, we utilize SPD matrices, ensuring data representation is well aligned with the quantum computational framework. Additionally, the method leverages polynomial feature expansion to capture nonlinear relationships within the data. The proposed pipeline combines classical fully connected neural network layers with quantum circuit layers to enhance model performance and efficiency. Our experiments focused on various configurations of such hybrid models to identify the optimal structure for accurate and efficient realtime analysis. The best performing model achieved a Mean Squared Error of 0.00031, significantly outperforming traditional methods.

翻译：桥梁的实时有限元建模通过提供结构完整性的全面洞察，辅助现代结构健康监测系统。该能力对于确保桥梁安全运行、防止突发灾难性失效至关重要。然而，有限元计算成本与实时分析需求构成重大挑战。此外，输入数据为七维向量，而输出为1017维向量，使得精确高效分析尤为困难。本研究提出一种新型混合量子经典多层感知机流水线，利用对称正定矩阵与黎曼流形实现高效数据表征。为保持量子比特结构完整性，我们采用SPD矩阵，确保数据表征与量子计算框架高度契合。同时，该方法通过多项式特征扩展捕捉数据中的非线性关系。所提流水线将经典全连接神经网络层与量子电路层相结合，以提升模型性能与效率。实验聚焦于不同配置的混合模型，旨在确定实现精确高效实时分析的最优结构。性能最优模型均方误差达0.00031，显著优于传统方法。