多序列：http://t.csdn.cn/yfjoh

数据在评论区，导入自己的数据即可预测并画图

%% 1.环境清理
clear, clc, close all;
%% 2.导入数据,单序列
D=readmatrix('B.xlsx');
data=D(:,2);%要求行向量
data1=data;
% 原始数据绘图
figure
plot(data,'-s','Color',[0 0 255]./255,'linewidth',1,'Markersize',5,'MarkerFaceColor',[0 0 255]./255)
legend('原始数据','Location','NorthWest','FontName','华文宋体');
xlabel('样本','fontsize',12,'FontName','华文宋体');
ylabel('数值','fontsize',12,'FontName','华文宋体');
%% 3.数据处理
nn=1500;%训练数据集大小
numTimeStepsTrain = floor(nn);%nn数据训练 ，N-nn个用来验证
[XTrain,YTrain,XTest,YTest,mu,sig] = shujuchuli(data,numTimeStepsTrain);
%% 4.定义LSTM结构参数
numFeatures= 1;%输入节点
numResponses = 1;%输出节点
numHiddenUnits = 500;%隐含层神经元节点数 
%构建 LSTM网络 
layers = [sequenceInputLayer(numFeatures) 
 lstmLayer(numHiddenUnits) %lstm函数 
dropoutLayer(0.2)%丢弃层概率 
 reluLayer('name','relu')% 激励函数 RELU 
fullyConnectedLayer(numResponses)
regressionLayer];
XTrain=XTrain';
YTrain=YTrain';
%% 5.定义LSTM函数参数 
def_options();
%% 6.训练LSTM网络 
net = trainNetwork(XTrain,YTrain,layers,options);
%% 7.建立训练模型 
net = predictAndUpdateState(net,XTrain);
%% 8.仿真预测(训练集) 
M = numel(XTrain);
for i = 1:M
    [net,YPred_1(:,i)] = predictAndUpdateState(net,XTrain(:,i),'ExecutionEnvironment','cpu');%
end
T_sim1 = sig*YPred_1 + mu;%预测结果去标准化 ，恢复原来的数量级 
%% 9.仿真预测(验证集) 
N = numel(XTest);
for i = 1:N
    [net,YPred_2(:,i)] = predictAndUpdateState(net,XTest(:,i),'ExecutionEnvironment','cpu');%
end
T_sim2 = sig*YPred_2 + mu;%预测结果去标准化 ，恢复原来的数量级 
%% 10.评价指标
%  均方根误差
T_train=data1(1:M)';
T_test=data1(M+1:end)';
error1 = sqrt(sum((T_sim1 - T_train).^2) ./ M);
error2 = sqrt(sum((T_sim2 - T_test ).^2) ./ N);
%  MAE
mae1 = sum(abs(T_sim1 - T_train)) ./ M ;
mae2 = sum(abs(T_sim2 - T_test )) ./ N ;
disp(['训练集数据的MAE为：', num2str(mae1)])
disp(['验证集数据的MAE为：', num2str(mae2)])
%  MAPE
maep1 = sum(abs(T_sim1 - T_train)./T_train) ./ M ;
maep2 = sum(abs(T_sim2 - T_test )./T_test) ./ N ;
disp(['训练集数据的MAPE为：', num2str(maep1)])
disp(['验证集数据的MAPE为：', num2str(maep2)])
%  RMSE
RMSE1 = sqrt(sumsqr(T_sim1 - T_train)/M);
RMSE2 = sqrt(sumsqr(T_sim2 - T_test)/N);
disp(['训练集数据的RMSE为：', num2str(RMSE1)])
disp(['验证集数据的RMSE为：', num2str(RMSE2)])
%% 11. 绘图
figure
subplot(2,1,1)
plot(T_sim1,'-s','Color',[255 0 0]./255,'linewidth',1,'Markersize',5,'MarkerFaceColor',[250 0 0]./255)
hold on 
plot(T_train,'-o','Color',[150 150 150]./255,'linewidth',0.8,'Markersize',4,'MarkerFaceColor',[150 150 150]./255)
legend( 'LSTM拟合训练数据','实际分析数据','Location','best');
title('LSTM模型预测结果及真实值','fontsize',12)
xlabel('样本','fontsize',12);
ylabel('数值','fontsize',12);
xlim([1 M])
%-------------------------------------------------------------------------------------
subplot(2,1,2)
bar((T_sim1 - T_train)./T_train)   
legend('LSTM模型训练集相对误差','Location','best')
title('LSTM模型训练集相对误差','fontsize',12)
ylabel('误差','fontsize',12)
xlabel('样本','fontsize',12)
xlim([1 M]);
%-------------------------------------------------------------------------------------
figure
subplot(2,1,1)
plot(T_sim2,'-s','Color',[0 0 255]./255,'linewidth',1,'Markersize',5,'MarkerFaceColor',[0 0 255]./255)
hold on 
plot(T_test,'-o','Color',[0 0 0]./255,'linewidth',0.8,'Markersize',4,'MarkerFaceColor',[0 0 0]./255)
legend('LSTM预测测试数据','实际分析数据','Location','best');
title('LSTM模型预测结果及真实值','fontsize',12)
xlabel('样本','fontsize',12);
ylabel('数值','fontsize',12);
xlim([1 N])
%-------------------------------------------------------------------------------------
subplot(2,1,2)
bar((T_sim2 - T_test )./T_test)   
legend('LSTM模型测试集相对误差','Location','NorthEast')
title('LSTM模型测试集相对误差','fontsize',12)
ylabel('误差','fontsize',12)
xlabel('样本','fontsize',12)
xlim([1 N]);
%% 12.预测未来
P = N-nn;% 预测未来数量
YPred_3 = [];%预测结果清零 
[T_sim3] = yuceweilai(net,XTrain,data,P,YPred_3,sig,mu)
%%  13.绘图
figure
plot(1:size(data,1),data,'-s','Color',[255 0 0]./255,'linewidth',1,'Markersize',5,'MarkerFaceColor',[250 0 0]./255)
hold on 
%plot(size(data,1)+1:size(data,1)+P,T_sim3,'-o','Color',[150 150 150]./255,'linewidth',0.8,'Markersize',4,'MarkerFaceColor',[150 150 150]./255)
legend( 'LSTM预测结果','Location','NorthWest');
title('LSTM模型预测结果','fontsize',12)
xlabel('样本','fontsize',12);
ylabel('数值','fontsize',12);

上面代码中对应的function函数：

shujuchuli.m

function [XTrain,YTrain,XTest,YTest,mu,sig] = shujuchuli(data,numTimeStepsTrain)
dataTrain = data(1:numTimeStepsTrain+1,:);% 训练样本
dataTest = data(numTimeStepsTrain:end,:); %验证样本 
%训练数据标准化处理 
mu = mean(dataTrain,'ALL');
sig = std(dataTrain,0,'ALL');
dataTrainStandardized = (dataTrain - mu) / sig;
XTrain = dataTrainStandardized(1:end-1,:);% 训练输入 
YTrain = dataTrainStandardized(2:end,:);% 训练输出
%测试样本标准化处理 
dataTestStandardized = (dataTest - mu) / sig;
XTest = dataTestStandardized(1:end-1,:)%测试输入 
YTest = dataTest(2:end,:);%测试输出 
XTest=XTest';
YTest=YTest';
end

yuceweilai.m

function [T_sim3] = yuceweilai(net,XTrain,data,P,YPred_3,sig,mu)
net1 = resetState(net);
net1 = predictAndUpdateState(net1,XTrain);
[net1,YPred_3] = predictAndUpdateState(net1,data(end));
for i = 2:P
    [net1,YPred_3(:,i)] = predictAndUpdateState(net1,YPred_3(:,i-1),'ExecutionEnvironment','cpu');
end
T_sim3 = sig*YPred_3 + mu;
end

def_options.m

options = trainingOptions('adam', ... % adam优化算法 自适应学习率 
'MaxEpochs',500,...% 最大迭代次数 
 'MiniBatchSize',10, ...%最小批处理数量 
'GradientThreshold',1, ...%防止梯度爆炸 
'InitialLearnRate',0.005, ...% 初始学习率 
'LearnRateSchedule','piecewise', ...
 'LearnRateDropPeriod',125, ...%125次后 ，学习率下降 
'LearnRateDropFactor',0.2, ...%下降因子 0.2
'ValidationData',{XTrain,YTrain}, ...
 'ValidationFrequency',5, ...%每五步验证一次 
'Verbose',1, ...
 'Plots','training-progress');

运行结果：