Hybrid Quantum Classical Surrogate for Real Time Inverse Finite Element Modeling in Digital Twins

TL;DR

This paper introduces a hybrid quantum-classical neural network framework that significantly improves real-time inverse finite element modeling for structural health monitoring, enabling faster and more accurate digital twin updates.

Contribution

The paper presents a novel hybrid quantum-classical multilayer perceptron that leverages quantum processing for large-scale inverse FE mapping in structural health monitoring.

Findings

Achieves extremely low mean squared error (MSE) of 3.16e-11, outperforming classical methods.

Demonstrates the feasibility of quantum-enhanced models for real-time structural diagnostics.

Provides a scalable approach for digital twin updates in civil infrastructure.

Abstract

Large-scale civil structures, such as bridges, pipelines, and offshore platforms, are vital to modern infrastructure, where unexpected failures can cause significant economic and safety repercussions. Although finite element (FE) modeling is widely used for real-time structural health monitoring (SHM), its high computational cost and the complexity of inverse FE analysis, where low dimensional sensor data must map onto high-dimensional displacement or stress fields pose ongoing challenges. Here, we propose a hybrid quantum classical multilayer perceptron (QMLP) framework to tackle these issues and facilitate swift updates to digital twins across a range of structural applications. Our approach embeds sensor data using symmetric positive definite (SPD) matrices and polynomial features, yielding a representation well suited to quantum processing. A parameterized quantum circuit (PQC) transforms these features, and the resultant quantum outputs feed into a classical neural network for final inference. By fusing quantum capabilities with classical modeling, the QMLP handles large scale inverse FE mapping while preserving computational viability. Through extensive experiments on a bridge, we demonstrate that the QMLP achieves a mean squared error (MSE) of 0.0000000000316, outperforming purely classical baselines with a large margin. These findings confirm the potential of quantum-enhanced methods for real time SHM, establishing a pathway toward more efficient, scalable digital twins that can robustly monitor and diagnose structural integrity in near real time.