MATLAB: Neural Network forecasting Issue

Deep Learning Toolboxforecastingneural networkprediction

Hello,
I've created a neural network to fit a certain (simple) input-output relationship. When I look at the time-series responses plot using the nntrain gui the predictions seem quite adequate, however, when I try to do out of sample prediction the results are nowhere close to the function being modelled.
I've googled this problem extensively and messed around with my code to no avail, I'd really appreciate a little insight into what I've been doing wrong.
I've included a minimal working example below.
 A = 1:1000;  B = 10000*sin(A); C = A.^2  +B;
Set = [A' B' C'];
input = Set(:,1:end-1);
target = Set(:,end);
inputSeries = tonndata(input(1:700,:),false,false);
targetSeries = tonndata(target(1:700,:),false,false);
%


inputSeriesVal = tonndata(input(701:end,:),false,false);
targetSeriesVal = tonndata(target(701:end,:),false,false);
%
inputDelays = 1:2;
feedbackDelays = 1:2;
hiddenLayerSize = 5;
net = narxnet(inputDelays,feedbackDelays,hiddenLayerSize);
%
[inputs,inputStates,layerStates,targets] = preparets(net,inputSeries,{},targetSeries);
net.divideFcn = 'divideblock';  % Divide data in blocks
net.divideMode = 'time';  % Divide up every value
 % Train the Network
[net,tr] = train(net,inputs,targets,inputStates,layerStates);
Y = net(inputs,inputStates,layerStates); 
 % Prediction Attempt
delay=length(inputDelays); N=300;
inputSeriesPred  = [inputSeries(end-delay+1:end),inputSeriesVal];
targetSeriesPred = [targetSeries(end-delay+1:end), con2seq(nan(1,N))];
netc = closeloop(net);
[Xs,Xi,Ai,Ts] = preparets(netc,inputSeriesPred,{},targetSeriesPred);
yPred = netc(Xs,Xi,Ai);
perf = perform(net,yPred,targetSeriesVal);
 figure;
plot([cell2mat(targetSeries),nan(1,N);
      nan(1,length(targetSeries)),cell2mat(yPred);
      nan(1,length(targetSeries)),cell2mat(targetSeriesVal)]')
legend('Original Targets','Network Predictions','Expected Outputs')
  end
I'd appreciate any insight into what I'm doing wrong,
Regards, James

Best Answer

You are using the wrong type of network for your problem.
Essentially you are trying to fit a function which is completely uncorrelated with itself, and you have no reason to use an Autoregressive network at all. You can choose a classical feedforward network to fit a function and forecast, it will do a much better job.
If you have a function where
C(n) = f(C(n-1),C(n-2),...)
NARX will make more sense.
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