【BP神经网络-非线性函数拟合】

x1 = linspace(-5,5,2000);
x2 = linspace(-5,5,2000);
y = x1.^2 + x2.^2;

Data classification

input = [x1;x2];
output = y;
k = rand(1,2000);
[m,n] = sort(k);

Training set

Input_Train = input(:,n(1:1900));
Output_Train = output(:,n(1:1900));

Test set

Input_Test = input(:,n(1901:end));
Output_Test = output(:,n(1901:end));

Training set normalization

[Input_Y,Input_PS] = mapminmax(Input_Train);
[Output_Y,Output_PS] = mapminmax(Output_Train);

Create BP neural network

net = newff(Input_Y,Output_Y,5);
net.trainParam.epochs = 100;
net.trainParam.lr = 0.1;
net.trainParam.goal = 0.00004;
net = train(net,Input_Y,Output_Y); % Training neural network

Test data normalization

Input_Y_Test = mapminmax('apply',Input_Test,Input_PS);
an = sim(net,Input_Y_Test);% Forecast output
BP_Output = mapminmax('reverse',an,Output_PS);% Output antinormalization

BP network prediction pattern

figure
plot(BP_Output,':og');
hold on;
plot(Output_Test,'-*');
legend('预测输出','期望输出');
title('BP网络预测输出','FontSize',12);
ylabel('函数输出',"FontSize",12);
xlabel('样本',"FontSize",12);

figure;
plot(BP_Output-Output_Test,'-*');
title('BP网络预测误差',"FontSize",12);
ylabel('误差',"FontSize",12);
xlabel('样本',"FontSize",12);