用梯度下降法建立bp神经网络 matlab代码

以下是用Matlab实现的基本BP神经网络模型，包括输入层、输出层和一个隐藏层，使用梯度下降法进行参数更新：

classdef BPNeuralNetwork
    properties
        input_size
        hidden_size
        output_size
        learning_rate
        w1
        b1
        w2
        b2
    end
    
    methods
        function obj = BPNeuralNetwork(input_size, hidden_size, output_size, learning_rate)
            obj.input_size = input_size;
            obj.hidden_size = hidden_size;
            obj.output_size = output_size;
            obj.learning_rate = learning_rate;
            
            % 初始化权重和偏置参数
            obj.w1 = randn(input_size, hidden_size);
            obj.b1 = zeros(1, hidden_size);
            obj.w2 = randn(hidden_size, output_size);
            obj.b2 = zeros(1, output_size);
        end
        
        function a = sigmoid(obj, x)
            a = 1 ./ (1 + exp(-x));
        end
        
        function y_pred = forward(obj, X)
            % 前向传播，计算每个神经元的输出值
            obj.z1 = X * obj.w1 + obj.b1;
            obj.a1 = obj.sigmoid(obj.z1);
            obj.z2 = obj.a1 * obj.w2 + obj.b2;
            obj.a2 = obj.sigmoid(obj.z2);
            y_pred = obj.a2;
        end
        
        function a = sigmoid_derivative(obj, x)
            a = x .* (1 - x);
        end
        
        function backward(obj, X, y, y_pred)
            % 反向传播，计算每个参数的梯度值
            obj.error = y - y_pred;
            obj.delta2 = obj.error .* obj.sigmoid_derivative(y_pred);
            obj.delta1 = obj.delta2 * obj.w2' .* obj.sigmoid_derivative(obj.a1);
            obj.w2 = obj.w2 + obj.learning_rate * obj.a1' * obj.delta2;
            obj.b2 = obj.b2 + obj.learning_rate * sum(obj.delta2, 1);
            obj.w1 = obj.w1 + obj.learning_rate * X' * obj.delta1;
            obj.b1 = obj.b1 + obj.learning_rate * sum(obj.delta1, 1);
        end
        
        function train(obj, X, y, epochs)
            for i = 1:epochs
                y_pred = obj.forward(X);
                obj.backward(X, y, y_pred);
            end
        end
        
        function y_pred = predict(obj, X)
            y_pred = obj.forward(X);
        end
    end
end

其中，`BPNeuralNetwork`类用于定义BP神经网络模型，`sigmoid`函数用于计算sigmoid激活函数的输出值，`forward`函数用于进行前向传播，`sigmoid_derivative`函数用于计算sigmoid函数的导数，`backward`函数用于进行反向传播，`train`函数用于训练网络，`predict`函数用于进行预测。在训练过程中，我们可以使用`train`函数对模型进行训练，并使用`predict`函数对新的数据进行预测。