  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.
