Machine Learning narx net optimization

Im am trying to predict a time serie from some data with a narx model.

I fit my model with 8 inputs (I also tried to vary that but it had not an impact on the result) and try to get an prediction model.

My trainingsdatas are:

Input [180000x8]

Ziel [180000x6] (or in english Target)

The goal is to predict the 6 targets.

An example what I mean with some random Numbers

Ziel=[1.0 0.5 2.0 1.0 2.0 1.5 sum[8.0

2.0 0.5 1.0 2.0 1.0 0.5 7.0

1.5 1.5 2.0 1.5 1.0 1.5 9.0

1.0 1.0 1.5 2.0 2.5 0.2 8.2

... ] ... ]

The main goal is that the sum of the prediciton is correct in each row but I also need the ratio in each row. Thats why I fit the model that way.

I tried to vary the delays and the hidden units. Also I tried it with normalization and with regularization (without normalization and regularization the calculation time increase enormously)

The "best" result of the below following code is (red is the prediction: sum(y_2n) and cyan the target: sum(Ziel))

This is my code: (I am using Matlab 2014a)

for j=3:100                                                              
X = tonndata(Input,false,false);                                          
T = tonndata(Ziel,false,false);                                        
trainFcn = 'trainlm';                                                    
inputDelays = 1:8;                                                         
feedbackDelays = 1:8;                                                      
hiddenLayerSize = j;                                                      
net = narxnet(inputDelays,feedbackDelays,hiddenLayerSize,'open',trainFcn); 
net.inputs{1}.processFcns = {'removeconstantrows','mapminmax'};
net.inputs{2}.processFcns = {'removeconstantrows','mapminmax'};
[x,xi,ai,t] = preparets(net,X,{},T);
net.divideFcn = 'divideind';                                               
net.divideMode = 'time';                                                   
Train_paramter=X_03_01_2008_date;
Valid_parameter=X_03_01_2009_date;
net.divideParam.trainInd = 1:Train_paramter;
net.divideParam.valInd = (Train_paramter+1):Valid_parameter;
net.divideParam.testInd = Valid_parameter+1:185440;

net.performFcn = 'mse';  
net.performParam.regularization = 0.5; %or without regularization
net.performParam.normalization='percent';%nothing or 'standart'
net.layers{1}.transferFcn='tansig';
net.layers{2}.transferFcn='purelin';
net.plotFcns = {'plotperform','plottrainstate','plotresponse', ...         
  'ploterrcorr', 'plotinerrcorr'};
[net,tr] = train(net,x,t,xi,ai);
[y,xfo,afo] = net(x,xi,ai);
%% Closed Loop Network
[netc,xic,aic] = closeloop(net,xfo,afo);                                   
[y2,xfc,afc] = netc(X,xic,aic);                                           
view(netc)                                        
y2_ns=cell2mat(y2);
figure, plotregression(Ziel,y2_ns');                     
figure(j+100)                                                             
plot(sum(Ziel')','c')
hold on
plot(sum(y2_ns),'r')
saveas(figure(j+100),sprintf('s100%d.png',j))
SaveName = sprintf('y2_n_2004_2010%d',j);
save(SaveName, 'y2_ns');
SaveName = sprintf('net%d',j);
save(SaveName, 'net');                                                     
net = init(net);
end