Leveraging SPD Matrices on Riemannian Manifolds in Quantum Classical Hybrid Models for Structural Health Monitoring
This work addresses computational efficiency and accuracy issues in structural health monitoring for bridge safety, representing an incremental improvement with specific domain application.
The study tackled the challenge of real-time finite element modeling for structural health monitoring by proposing a hybrid quantum-classical MLP pipeline using SPD matrices on Riemannian manifolds, achieving a Mean Squared Error of 0.00031 that significantly outperformed traditional methods.
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.