Issue using LSTM neural network "Time Series Forecasting Using Deep Learning"

I am trying to use the LSTM regression

https://au.mathworks.com/help/deeplearning/ug/time-series-forecasting-using-deep-learning.html

The code:

%%Load Sequence Data
%Input data
S=xlsread("AVcigs.csv","AVcigs","C7:C56385");
%Output data
Pmpp=xlsread("AVcigs.csv","AVcigs","F7:F56385");
for i=1:length(Pmpp)
    if Pmpp(i) <0
        Pmpp(i)=0;
    else
        Pmpp(i)=Pmpp(i);
    end
end        

%Partition the training and test data.
numTimeStepsTrain = floor(0.7*numel(S));
dataTrain_S = S(1:numTimeStepsTrain+1);
dataTest_S = S(numTimeStepsTrain+1:end);

dataTrain_Pmpp = Pmpp(1:numTimeStepsTrain+1);
dataTest_Pmpp = Pmpp(numTimeStepsTrain+1:end);

%%Standardize Data
mu_S = mean(dataTrain_S);
sig_S = std(dataTrain_S);
dataTrainStandardized_S = (dataTrain_S - mu_S) / sig_S;

mu_Pmpp = mean(dataTrain_Pmpp);
sig_Pmpp = std(dataTrain_Pmpp);
dataTrainStandardized_Pmpp = (dataTrain_Pmpp - mu_Pmpp) / sig_Pmpp;

%%Prepare Predictors and Responses
XTrain = dataTrainStandardized_S(1:end-1);
XTrain = XTrain';
YTrain = dataTrainStandardized_Pmpp(1:end-1);
YTrain = YTrain';
for i=1:length(YTrain)
    if YTrain(i) <0
        YTrain(i)=0;
    else
        YTrain(i)=YTrain(i);
    end
end
%%Define LSTM Network Architecture
numFeatures = 1;
numResponses = 1;
numHiddenUnits = 200;

layers = [ ...
    sequenceInputLayer(numFeatures)
    lstmLayer(numHiddenUnits)
    fullyConnectedLayer(numResponses)
    regressionLayer];

options = trainingOptions('adam', ...
    'MaxEpochs',250, ...
    'GradientThreshold',1, ...
    'InitialLearnRate',0.005, ...
    'LearnRateSchedule','piecewise', ...
    'LearnRateDropPeriod',125, ...
    'LearnRateDropFactor',0.2, ...
    'Verbose',0, ...
    'Plots','training-progress');

%%Train LSTM Network
net = trainNetwork(XTrain,YTrain,layers,options);

%%Forecast Future Time Steps
%Standardize the test data using the same parameters as the training data.
dataTestStandardized_S = (dataTest_S - mu_S) / sig_S;
dataTrainStandardized_Pmpp = (dataTest_Pmpp - mu_Pmpp) / sig_Pmpp;

net = predictAndUpdateState(net,XTrain);
[net,YPred] = predictAndUpdateState(net,YTrain(end));

YPred = sig_Pmpp*YPred + mu_Pmpp;

XTest=dataTestStandardized_S(1:end-1);
XTest=XTest';
YTest = dataTrainStandardized_Pmpp(1:end-1);
YTest = YTest';

for i=1:length(YTest)
    if YTest(i) <0
        YTest(i)=0;
    else
        YTest(i)=YTest(i);
    end
end

numTimeStepsTest = numel(XTest);
for i = 2:numTimeStepsTest
    [net,YPred(:,i)] = predictAndUpdateState(net,YPred(:,i-1),'ExecutionEnvironment','gpu');
end

YTest = Pmpp(2:end);
rmse = sqrt(mean((YPred-YTest).^2))


figure(1)
plot(dataTrain_Pmpp(1:end-1))
hold on
idx = numTimeStepsTrain:(numTimeStepsTrain+numTimeStepsTest);
plot(idx,[Pmpp(numTimeStepsTrain) YPred],'.-')
hold off
xlabel("Time")
ylabel("Pmpp")
title("Forecast")
legend(["Observed" "Forecast"])

figure(2)
subplot(2,1,1)
plot(YTest)
hold on
plot(YPred,'.-')
hold off
legend(["Observed" "Forecast"])
ylabel("Pmpp")
title("Forecast")

subplot(2,1,2)
stem(YPred - YTest)
xlabel("time")
ylabel("Error")
title("RMSE = " + rmse)

%%Update Network State with Observed Values
net = resetState(net);
net = predictAndUpdateState(net,XTrain);

YPred = [];
numTimeStepsTest = numel(XTest);
for i = 1:numTimeStepsTest
    [net,YPred(:,i)] = predictAndUpdateState(net,XTest(:,i),'ExecutionEnvironment','cpu');
end
YPred = sig_Pmpp*YPred + mu_Pmpp;

rmse = sqrt(mean((YPred-YTest).^2))

figure (3)
subplot(2,1,1)
plot(YTest)
hold on
plot(YPred,'.-')
hold off
legend(["Observed" "Predicted"])
ylabel("Pmpp")
title("Forecast with Updates")

subplot(2,1,2)
stem(YPred - YTest)
xlabel("Time")
ylabel("Error")
title("RMSE = " + rmse)

I keep having the following error:

Out of memory.
Error in stem (line 104)
            h(k) = matlab.graphics.chart.primitive.Stem('Parent', parax, 'YData',matlab.graphics.chart.internal.datachk(y(:,k)),
            xdata{:},...

Error in LSTM_onefeature (line 150)
stem(YPred - YTest)

Answer 1

[Srivardhan Gadila]

As we can see from the error message " Out of memory. Error in stem (line 104)

h(k) = matlab.graphics.chart.primitive.Stem('Parent', parax, 'YData',matlab.graphics.chart.internal.datachk(y(:,k)), xdata{:},..."

I think that the issue is w.r.t the size of YTest & YPred.

Try the plot and stem functions for subset of YTest & YPred i.e.,

 stem(YPred(1:10) - YTest(1:10))

and check whether you are still facing the issue or not.

The "Out of memory" issue with stem function is similar to the "Out of Memory" issue of the following MATLAB Answer: Why do I receive an "Out of Memory" error when I attempt to render a surface with a large number of data points in MATLAB?