Quantum‐Classical Physics‐Informed Neural Networks for Permeability Inversion in Single‐Phase Reservoir Flow

ABSTRACT

This work develops a Quantum‐Classical Physics‐Informed Neural Network (QCPINN) integrating quantum computing and physical constraints for single‐phase reservoir permeability inversion. The hybrid framework contains classical pre/post‐processing modules and an Alternate‐topology quantum core, which encodes spatial features through angle embedding and optimizes all hybrid parameters using a composite loss combining measurement, PDE residual and boundary condition losses. Two steady seepage examples compare QCPINN and classical PINN with nearly identical trainable parameters. For linear permeability, QCPINN achieves mean relative errors of 0.50% for permeability and 0.04% for pressure, converging faster with more uniform errors; 4 qubits and one layer provide optimal circuit performance. For strongly nonlinear exponential permeability, the permeability mean relative error rises to 5.02%, while pressure error stays below 0.42%. Although isolated low‐permeability grids show a peak relative error of 48.13%, 78.68% of grids have errors under 5%. QCPINN takes advantage of quantum high‐dimensional approximation and parallelism to outperform PINN in convergence and precision, delivering balanced accuracy and efficiency for heterogeneous reservoir permeability inversion.