[2512.03923] Quantum-Classical Physics-Informed Neural Networks for Solving Reservoir Seepage Equations

Computer Science > Machine Learning arXiv:2512.03923 (cs) [Submitted on 3 Dec 2025 (v1), last revised 25 Mar 2026 (this version, v2)] Title:Quantum-Classical Physics-Informed Neural Networks for Solving Reservoir Seepage Equations Authors:Xiang Rao, Yina Liu, Yuxuan Shen View a PDF of the paper titled Quantum-Classical Physics-Informed Neural Networks for Solving Reservoir Seepage Equations, by Xiang Rao and 2 other authors View PDF Abstract:In this paper, we adapt the Discrete Variable (DV)-Circuit Quantum-Classical Physics-Informed Neural Network (QCPINN) and apply it for the first time to four typical reservoir seepage models. These include the pressure diffusion equation for heterogeneous single-phase flow, the nonlinear Buckley-Leverett (BL) equation for simplified two-phase waterflooding, the convection-diffusion equation for compositional flow considering adsorption, and the fully coupled pressure-saturation two-phase oil-water seepage equation for heterogeneous reservoirs with exponential permeability distribution. 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 four numerical experiments that QCPINNs achieve higher prediction accuracy than classical PINNs. Specif...