The solution of matrix eigenvalues has always been a research hotspot in the field of modern numerical analysis, which has important value in practical application of engineering technology and scientific research. Despite the fact that currently existing algorithms for solving the eigenvalues of matrices are well-developed to try to satisfy both in terms of computational accuracy and efficiency, few of them have been able to be realized on photonic platform. The photonic neural network not only has strong judgment in solving inference tasks due to the superior learning ability, but also makes full use of the advantages of photonic computing with ultrahigh speed and ultralow energy consumption. Here, we propose a strategy of an eigenvalue solver for real-value symmetric matrices based on reconfigurable photonic neural networks. The strategy shows the feasibility of solving the eigenvalues of real-value symmetric matrices of n × n matrices with locally connected networks. Experimentally, we demonstrate the task of solving the eigenvalues of 2 × 2, 3 × 3, and 4 × 4 real-value symmetric matrices based on graphene/Si thermo-optical modulated reconfigurable photonic neural networks with saturated absorption nonlinear activation layer. The theoretically predicted test set accuracy of the 2 × 2 matrices is 93.6% with the measured accuracy of 78.8% in the experiment by the standard defined for simplicity of comparison. This work not only provides a feasible solution for the on-chip integrated photonic realization of eigenvalue solving of real-value symmetric matrices, but also lays the foundation for a new generation of intelligent on-chip integrated all-optical computing.

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基于可重构光子神经网络的矩阵特征值求解器

矩阵特征值的求解一直是现代数值分析领域的研究热点，在工程技术和科学研究的实际应用中具有重要价值。尽管目前用于求解矩阵特征值的现有算法已经很好地开发，试图在计算精度和效率方面都满足，但其中很少有能够在光子平台上实现。光子神经网络不仅具有超强的学习能力，在解决推理任务方面具有很强的判断力，而且还充分利用了光子计算的超高速、超低能耗的优势。在这里，我们提出了一种基于可重构光子神经网络的实值对称矩阵的特征值求解器策略。n×n具有本地连接网络的矩阵。在实验上，我们展示了基于具有饱和吸收非线性激活层的石墨烯/Si 热光调制可重构光子神经网络求解 2 × 2、3 × 3 和 4 × 4 实值对称矩阵的特征值的任务。2 × 2 矩阵的理论预测测试集准确率为 93.6%，按照为简化比较而定义的标准，在实验中测得的准确率为 78.8%。该工作不仅为实值对称矩阵特征值求解的片上集成光子实现提供了可行的解决方案，也为新一代智能片上集成全光计算奠定了基础。