Zuyu Xu

Zuyu Xu, Kang Shen, Pengnian Cai et al.

The recent emergence of the hybrid quantum-classical neural network (HQCNN) architecture has garnered considerable attention due to the potential advantages associated with integrating quantum principles to enhance various facets of machine learning algorithms and computations. However, the current investigated serial structure of HQCNN, wherein information sequentially passes from one network to another, often imposes limitations on the trainability and expressivity of the network. In this study, we introduce a novel architecture termed Parallel Proportional Fusion of Quantum and Spiking Neural Networks (PPF-QSNN). The dataset information is simultaneously fed into both the spiking neural network and the variational quantum circuits, with the outputs amalgamated in proportion to their individual contributions. We systematically assess the impact of diverse PPF-QSNN parameters on network performance for image classification, aiming to identify the optimal configuration. Numerical results on the MNIST dataset unequivocally illustrate that our proposed PPF-QSNN outperforms both the existing spiking neural network and the serial quantum neural network across metrics such as accuracy, loss, and robustness. This study introduces a novel and effective amalgamation approach for HQCNN, thereby laying the groundwork for the advancement and application of quantum advantage in artificial intelligent computations.

Zuyu Xu, Bin Lv

Neural networks have emerged as powerful tools for modeling complex physical systems, yet balancing high accuracy with computational efficiency remains a critical challenge in their convergence behavior. In this work, we propose the Hybrid Parallel Kolmogorov-Arnold Network (KAN) and Multi-Layer Perceptron (MLP) Physics-Informed Neural Network (HPKM-PINN), a novel architecture that synergistically integrates parallelized KAN and MLP branches within a unified PINN framework. The HPKM-PINN introduces a scaling factor ξ, to optimally balance the complementary strengths of KAN's interpretable function approximation and MLP's nonlinear feature learning, thereby enhancing predictive performance through a weighted fusion of their outputs. Through systematic numerical evaluations, we elucidate the impact of the scaling factor ξ on the model's performance in both function approximation and partial differential equation (PDE) solving tasks. Benchmark experiments across canonical PDEs, such as the Poisson and Advection equations, demonstrate that HPKM-PINN achieves a marked decrease in loss values (reducing relative error by two orders of magnitude) compared to standalone KAN or MLP models. Furthermore, the framework exhibits numerical stability and robustness when applied to various physical systems. These findings highlight the HPKM-PINN's ability to leverage KAN's interpretability and MLP's expressivity, positioning it as a versatile and scalable tool for solving complex PDE-driven problems in computational science and engineering.