发表机构
National Laboratory of Scientific Computing; Center for Computation and Technology - Louisiana State University（国家科学计算实验室; 路易斯安那州立大学计算与技术中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出混合量子-经典框架，通过自适应采样、损失加权等策略增强QPINNs，在基准流体等系统中解精度提升至少60%，为量子增强科学机器学习提供可扩展途径。
AI 中文摘要
物理信息神经网络（PINNs）已成为求解非线性偏微分方程（PDE）的通用方法，但对于高维或多尺度系统，高效实现高精度仍具挑战性。本文提出一种混合量子-经典框架，通过自适应配置点采样和感知损失的注意力机制增强量子物理信息神经网络（QPINNs）。该方法动态优先选择PDE残差大或解梯度陡峭区域的点，缓解了传统PINNs固有的谱偏差。现有量子物理信息神经网络常被认为受限于量子电路的表达能力，而本文研究发现，在多种微分方程中，优化而非仅表达能力是重要瓶颈。此外，可训练的损失加权方案在训练期间平衡物理残差、边界条件和数据保真度的贡献。将这些策略与量子计算技术（包括变分量子电路和量子梯度估计）相结合，在特定工况下可使基准流体流动和反应扩散系统的解精度提升至少60%。最后，本文指出，仅增加QPINNs的模型表达能力不足以求解复杂PDE，因为其仍受限于传统PINNs的结构优化局限。该框架为量子增强的科学机器学习提供了可扩展途径，将基于物理的建模与新兴量子计算能力相结合。
英文摘要
Physics-informed neural networks (PINNs) have emerged as a versatile approach for solving nonlinear partial differential equations (PDEs), yet achieving high accuracy efficiently using these techniques remains challenging for high-dimensional or multiscale systems. Here, we present a hybrid quantum-classical framework that enhances Quantum PINNs (QPINNs) through adaptive collocation point sampling and loss-aware attention mechanisms. By dynamically prioritizing points in regions with large PDE residuals or steep solution gradients, our method mitigates the spectral bias inherent in conventional PINNs. Current Quantum Physics-Informed Neural Networks are commonly assumed to be limited by the expressive power of quantum circuits. In our work, we observed that, across diverse differential equations, optimization - not only expressivity - can be an important bottleneck. Furthermore, a trainable loss-weighting scheme balances contributions from physics residuals, boundary conditions, and data fidelity during training. Integrating these strategies with quantum computing techniques (including variational quantum circuits and quantum gradient estimation) can yield at least a 60% improvement in solution accuracy under specific regimes for benchmark fluid flows and reaction-diffusion systems. Finally, we argue that merely increasing model expressivity is insufficient for resolving complex PDEs via QPINNs, as they remain constrained by the structural optimization limitations of classical PINNs. This framework provides a scalable pathway for quantum-enhanced scientific machine learning, bridging physics-based modeling with emerging quantum computational capabilities.
