LSTM Neural Network Time Series Prediction

Given a simple dataset, we use Long Short-Term Memory (LSTM) neural networks to implement time series prediction, with the ReLU function as the activation function. The implementation code is as follows:

Part 1. Time Series Prediction Implementation

% LSTM Neural Network Time Series Prediction
clear,clc
res = xlsread('dataset.xlsx');
temp = randperm(103);

P_train = res(temp(1: 80), 1: 7)';
T_train = res(temp(1: 80), 8)';
M = size(P_train, 2);

P_test = res(temp(81: end), 1: 7)';
T_test = res(temp(81: end), 8)';
N = size(P_test, 2);

[P_train, ps_input] = mapminmax(P_train, 0, 1);
P_test = mapminmax('apply', P_test, ps_input);

t_train, ps_output] = mapminmax(T_train, 0, 1);
t_test = mapminmax('apply', T_test, ps_output);

P_train =  double(reshape(P_train, 7, 1, 1, M));
P_test  =  double(reshape(P_test , 7, 1, 1, N));

t_train = t_train';
t_test  = t_test' ;

for i = 1 : M
    p_train{i, 1} = P_train(:, :, 1, i);
end

for i = 1 : N
    p_test{i, 1}  = P_test( :, :, 1, i);
end

layers = [
    sequenceInputLayer(7)              
    lstmLayer(4, 'OutputMode', 'last') 
    reluLayer                            
    fullyConnectedLayer(1)             
    regressionLayer];                  
 
options = trainingOptions('adam', ...    
    'MaxEpochs', 1500, ...               
    'InitialLearnRate', 0.01, ...         
    'LearnRateSchedule', 'piecewise', ... 
    'LearnRateDropFactor', 0.1, ...       
    'LearnRateDropPeriod', 1200, ...      
    'Shuffle', 'every-epoch', ...          
    'Plots', 'training-progress', ...      
    'Verbose', false);

net = trainNetwork(p_train, t_train, layers, options);
t_sim1 = predict(net, p_train);
t_sim2 = predict(net, p_test );
T_sim1 = mapminmax('reverse', t_sim1, ps_output);
T_sim2 = mapminmax('reverse', t_sim2, ps_output);

error1 = sqrt(sum((T_sim1' - T_train).^2) ./ M);
error2 = sqrt(sum((T_sim2' - T_test ).^2) ./ N);
analyzeNetwork(net)

figure
plot(1: M, T_train, 'g--+', 1: M, T_sim1, 'r-o', 'LineWidth', 1)
legend('True Values', 'Predicted Values')
xlabel('Predicted Samples')
ylabel('Prediction Results')
string = {'Training Set Prediction Results Comparison'; ['RMSE=' num2str(error1)]};
title(string)
xlim([1, M])
grid

figure
plot(1: N, T_test, 'r--x', 1: N, T_sim2, 'm-^', 'LineWidth', 1)
legend('True Values', 'Predicted Values')
xlabel('Predicted Samples')
ylabel('Prediction Results')
string = {'Test Set Prediction Results Comparison'; ['RMSE=' num2str(error2)]};
title(string)
xlim([1, N])
grid

R1 = 1 - norm(T_train - T_sim1')^2 / norm(T_train - mean(T_train))^2;
R2 = 1 - norm(T_test  - T_sim2')^2 / norm(T_test  - mean(T_test ))^2;

disp(['Training Set R2:', num2str(R1)])
disp(['Test Set R2:', num2str(R2)])

mae1 = sum(abs(T_sim1' - T_train)) ./ M ;
mae2 = sum(abs(T_sim2' - T_test )) ./ N ;

disp(['Training Set MAE:', num2str(mae1)])
disp(['Test Set MAE:', num2str(mae2)])

mbe1 = sum(T_sim1' - T_train) ./ M ;
mbe2 = sum(T_sim2' - T_test ) ./ N ;

disp(['Training Set MBE:', num2str(mbe1)])
disp(['Test Set MBE:', num2str(mbe2)])

sz = 25;
c = 'r';

figure
scatter(T_train, T_sim1, sz, c)
hold on
plot(xlim, ylim, '--k')
xlabel('Training Set True Values');
ylabel('Training Set Predicted Values');
xlim([min(T_train) max(T_train)])
ylim([min(T_sim1) max(T_sim1)])
title('Training Set Predicted Values & True Values')

figure
scatter(T_test, T_sim2, sz, c)
hold on
plot(xlim, ylim, '--k')
xlabel('Test Set True Values');
ylabel('Test Set Predicted Values');
xlim([min(T_test) max(T_test)])
ylim([min(T_sim2) max(T_sim2)])
title('Test Set Predicted Values & True Values')

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Part 2. Plotting Results Display

Part 2. Resource Acquisition:

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