全光神经网络的matlab仿真

论文总字数：51028字

摘 要

神经网络使得计算机可以执行更高级更复杂的任务。传统神经网络输入端通常利用实数携带信息，相邻层之间的神经元之间的连接以实数权重表示，在神经元处通常采用Sigmoid、ReLU等线性函数或其他非线性函数对输入信息进行处理，再输出。而光学神经网络，仅仅是利用了神经网络的思路，输入端可以是复数，传播过程则是利用了光学传播方法。相比于传统网络，由于信息是以光传播的，并且光具有并行计算的能力，光学神经网络处理速度更快。此外，光学神经网络中使用的光学元件是无源器件，无需额外的能量供应，能耗比传统电子电路更低。高效、节能的优良性质使光学神经网络具有一定的研究价值。

本文在MATLAB平台上，构建仿真了一个光学神经网络，编写程序模拟光学衍射过程，通过训练调节光学传播过程中的相关参数，以提高网络执行相关功能的能力。

关键词：神经网络，光学衍射，手写数字，仿真

Abstract

Neural networks enable computers to perform more advanced and more complex tasks. We usually input real numbers into traditional neural network, which carry information. The connections between neurons between adjacent layers are represented by real weights. At the neuron, linear functions such as Sigmoid and ReLU or other nonlinear functions are usually used to process input information and then output the result. The optical neural network is similar to the traditional neural network. However, the input end can be a complex number, and the propagation process utilizes optical propagation methods. Compared to traditional networks, optical neural networks process faster because information is transmitted by light and the light has the ability to be parallelized. In addition, the optical components used in optical neural networks are passive devices that require no additional energy supply and consume less energy than traditional electronic circuits. The excellent properties of high efficiency and energy saving make the optical neural network have certain research value.

In this paper, an optical neural network is constructed and simulated on the MATLAB platform. The program simulates the optical diffraction process and adjusts the relevant parameters in the optical propagation process to improve the ability of the network to perform related functions.

KEY WORDS: neural network, optical diffraction, handwritten numbers, simulation

目 录

摘要 ……………………………………………………………………………………………….Ⅰ

Abstract ………………………………………………………………………………………….Ⅰ

1. 绪论 …………………………………………………………………………………….1

1.1 引言 ………………………………………………………………………………….1

1.2 光学神经网络的发展 …………………………………………………………….2

1.3 光神经网络的应用 ……………………………………………………………….4

1.4 本文的研究目的和主要研究内容 ……………………………………………..4

1. 光学衍射 ……………………………………………………………………………..6

2.1 数学预备知识 ……………………………………………………………………..6

2.1.1 亥姆霍兹方程 …………………………………………………………..6

2.1.2 格林定理 ………………………………………………………………...6

2.1.3 亥姆霍兹与基尔霍夫的积分定理 ………………………………….6

2.2 基尔霍夫理论 …………………………………………………………………….8

2.3 瑞利-索末菲衍射 ………………………………………………………………...9

2.4 基尔霍夫衍射公式与瑞利-索末菲衍射公式的比较 ……………………..11

2.5 惠更斯-菲涅尔原理在直角坐标系中的表述 ………………………………11

1. 神经网络 …………………………………………………………………………….13

3.1 神经元模型 ……………………………………………………………………….13

3.2 感知机和深层网络 ……………………………………………………………...13

3.3 误差反向传播算法 ……………………………………………………………...15

3.4 SGD， Batch和Mini Batch算法 ……………………………………………18

3.4.1 SGD算法 ………………………………………………………………..18

3.4.2 Batch算法 ………………………………………………………………18

3.4.3 Mini Batch算法 ………………………………………………………..19

1. 光学神经网络的仿真 ……………………………………………………………..20

4.1 MNIST手写数字数据库 …………………………………………………….20

4.2 光学衍射网络的构建 ………………………………………………………..20

4.2.1 输入 ……………………………………………………………………...20

4.2.2 衍射网络 ………………………………………………………………..20

4.2.3 参数更新 ………………………………………………………………..22

4.3 训练结果与分析 ……………………………………………………………...23

总结 ……………………………………………………………………………………………...27

参考文献（References） ……………………………………………………………………...28

附录一 程序清单与程序流程图 …………………………………………………………...29

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