Leveraging SPD Matrices on Riemannian Manifolds in Quantum Classical Hybrid Models for Structural Health Monitoring

TL;DR

This paper introduces a hybrid quantum-classical neural network using SPD matrices on Riemannian manifolds for real-time structural health monitoring, achieving high accuracy and efficiency in bridge FEM analysis.

Contribution

The study presents a novel hybrid quantum-classical MLP pipeline utilizing SPD matrices and Riemannian geometry, enhancing real-time structural health monitoring capabilities.

Findings

Achieved a Mean Squared Error of 0.00031 with the best model.

Outperformed traditional methods in accuracy and efficiency.

Effectively captured nonlinear relationships in high-dimensional data.

Abstract

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.