Quantum-Classical Physics-Informed Neural Networks for Solving Reservoir Seepage Equations

Abstract: Solving partial differential equations (PDEs) for reservoir seepage is critical for optimizing oil and gas field development and predicting production performance. Traditional numerical methods suffer from mesh-dependent errors and high computational costs, while classical Physics-Informed Neural Networks (PINNs) face bottlenecks in parameter efficiency, high-dimensional expression, and strong nonlinear fitting. To address these limitations, we propose a Discrete Variable (DV)-Circuit Quantum-Classical Physics-Informed Neural Network (QCPINN) and apply it to three typical reservoir seepage models for the first time: the pressure diffusion equation for heterogeneous single-phase flow, the nonlinear Buckley-Leverett (BL) equation for two-phase waterflooding, and the convection-diffusion equation for compositional flow considering adsorption. The QCPINN integrates classical preprocessing/postprocessing networks with a DV quantum core, leveraging quantum superposition and entanglement to enhance high-dimensional feature mapping while embedding physical constraints to ensure solution consistency. We test three quantum circuit topologies (Cascade, Cross-mesh, Alternate) and demonstrate through numerical experiments that QCPINNs achieve high prediction accuracy with fewer parameters than classical PINNs. Specifically, the Alternate topology outperforms others in heterogeneous single-phase flow and two-phase BL equation simulations, while the Cascade topology excels in compositional flow with convection-dispersion-adsorption coupling. Our work verifies the feasibility of QCPINN for reservoir engineering applications, bridging the gap between quantum computing research and industrial practice in oil and gas engineering.