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<p>This study presents a hybrid variational quantum-classical neural network (VQNN) to predict two geotechnical parameters related to seismic site characterisation based on the cone penetration test (CPT): directly measured shear wave velocity (Vs) from seismic CPT and the Robertson soil behaviour type index (Ic SBT). From an Austrian database, after filtering, 1,879 SCPT samples were retained for the Vs target, and 5,000 records were retained for the Ic SBT target. The hybrid architecture comprised a 3-qubit parameterised quantum circuit with angle embedding and two strongly entangling layers, and classical pre- and post-processing networks; all parameters were trained simultaneously using L-BFGS-B optimisation on a principal-component-reduced feature space. The VQNN was compared with an artificial neural network, a random forest, and a gradient boosting machine using 5-fold cross-validation and eight performance metrics (R², RMSE, MAE, MAPE, A10 − I, SI, IA, KGE). For Ic, SBT classical models achieved near-perfect accuracy (R2 &gt; 0.999); VQNN achieved R<sup>2</sup> = 0.900, IA = 0.973. Classical models achieved R<sup>2</sup> = 0.46–0.48 for directly measured Vs, whereas VQNN achieved R<sup>2</sup> = 0.207. Wilcoxon signed-rank tests confirmed significant differences among models (<i>p</i> &lt; 0.05). Depth, pore pressure and sleeve friction were highlighted as dominant Vs predictors by permutation feature importance.</p>

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A Hybrid Variational Quantum-Classical Neural Network for CPT-Based Prediction of Shear Wave Velocity and Soil Behaviour Type Index

  • 期刊论文

  • 发表日期：

    2026年6月17日

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  • Omer Muhie Eldeen Taha,
  • Sarah Mustafa Ahmed

摘要

This study presents a hybrid variational quantum-classical neural network (VQNN) to predict two geotechnical parameters related to seismic site characterisation based on the cone penetration test (CPT): directly measured shear wave velocity (Vs) from seismic CPT and the Robertson soil behaviour type index (Ic SBT). From an Austrian database, after filtering, 1,879 SCPT samples were retained for the Vs target, and 5,000 records were retained for the Ic SBT target. The hybrid architecture comprised a 3-qubit parameterised quantum circuit with angle embedding and two strongly entangling layers, and classical pre- and post-processing networks; all parameters were trained simultaneously using L-BFGS-B optimisation on a principal-component-reduced feature space. The VQNN was compared with an artificial neural network, a random forest, and a gradient boosting machine using 5-fold cross-validation and eight performance metrics (R², RMSE, MAE, MAPE, A10 − I, SI, IA, KGE). For Ic, SBT classical models achieved near-perfect accuracy (R2 > 0.999); VQNN achieved R2 = 0.900, IA = 0.973. Classical models achieved R2 = 0.46–0.48 for directly measured Vs, whereas VQNN achieved R2 = 0.207. Wilcoxon signed-rank tests confirmed significant differences among models (p < 0.05). Depth, pore pressure and sleeve friction were highlighted as dominant Vs predictors by permutation feature importance.