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

Abstract:Solving reservoir seepage partial differential equations (PDEs) is critical for hydrocarbon development optimization and production forecasting. Conventional numerical solvers suffer from mesh errors and high computational cost. Standard Physics-Informed Neural Networks (PINNs) are limited by inefficient parameters. They also face weak high-dimensional representation and poor nonlinear fitting ability. We adapt the Discrete Variable (DV)-Circuit Quantum-Classical Physics-Informed Neural Network (QCPINN) to tackle these drawbacks. This work applies the method to four representative reservoir seepage models. The models cover heterogeneous single-phase pressure diffusion. They also include nonlinear Buckley-Leverett two-phase waterflooding. Another case is adsorption-coupled convection-diffusion compositional flow. The last one refers to fully coupled pressure-saturation two-phase flow with exponential permeability heterogeneity. The QCPINN combines classical preprocessing and postprocessing networks with a DV quantum core. It leverages quantum entanglement and superposition to boost high-dimensional feature mapping. Physical constraints are embedded within the framework to guarantee physically consistent solutions. We evaluate three quantum circuit topologies including Cascade, Cross-mesh and Alternate. Numerical tests prove QCPINNs outperform classical PINNs in prediction accuracy, and the circuit topologies show case-specific performance with clear applicable ranges. This work verifies QCPINN's practicability for reservoir engineering. It bridges quantum computing research with oilfield industrial applications.

Machine Learning (cs.LG); Numerical Analysis (math.NA); Computational Physics (physics.comp-ph)

arXiv:2512.03923 [cs.LG]

(or arXiv:2512.03923v3 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2512.03923 Focus to learn more arXiv-issued DOI via DataCite

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