这篇论文发布了QCPIKAN，首个混合量子经典PDE求解器，用Chebyshev KAN层加速收敛，渗流模拟精度远超市面同类。
研究者提出QCPIKAN，这是首个量子-经典物理信息Kolmogorov-Arnold网络，采用Chebyshev多项式KAN层和参数化量子电路。理论证明该设计能使高频误差以指数率收敛，并有效抑制数值色散。在三种典型渗流场景（单相流、组分输送、两相流）中验证。相比现有量子-经典物理信息神经网络，QCPIKAN在全局预测精度、局部误差控制、动态演化跟踪和位移前沿定位上表现更优。
Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs
We develop QCPIKAN, the first quantum-classical physics-informed Kolmogorov-Arnold network designed to solve partial differential equations (PDEs). Built upon Chebyshev-polynomial KAN layers and parameterized quantum circuits, this hybrid framework embeds physical constraints into the training loss to enforce physical consistency. Our theoretical investigations grounded in approximation theory prove that this design accelerates high-frequency error convergence to an exponential rate and effectively mitigates numerical dispersion. We validate the framework across three typical seepage scenarios in porous media, including single-phase flow, component transport and two-phase flow. Compared with existing quantum-classical physics-informed neural networks, QCPIKAN achieves superior performance in global prediction accuracy, local error control, dynamic evolution tracking and displacement front localization. This work provides a robust and efficient alternative for solving complex PDEs.