Neural Network for predictions. How to improve it

 Hi everyone,

I am trying to build a code with the NN toolbox, able to predict at time t+2 the Manganese content in a reservoir, given as inputs other 7 variables (among these, also the Mn at time t=0).

 

While I am waiting for far more data, which definitely will improve the performance, I am trying to play with the several options through the network to improve it. You find the code below:

 

 

_  inputs = Inputs7old';
  targets = Mnt2old';

% Create a Fitting Network
hiddenLayerSize = 10;
FIT1 = fitnet(hiddenLayerSize);
FIT1.numLayers = 3;
FIT1.layers{2}.name='Hidden2';
FIT1.layers{3}.name='Output';
FIT1.layers{2}.dimensions=10;
FIT1.layers{3}.dimensions=1;
FIT1.inputConnect = [1; 0; 0];
FIT1.layerConnect = [0 0 0;1 0 0;1 1 0];
FIT1.outputConnect = [0 0 1];

% Choose Input and Output Pre/Post-Processing Functions
% For a list of all processing functions type: help nnprocess
FIT1.inputs{1}.processFcns = {'removeconstantrows','mapminmax'};
FIT1.outputs{2}.processFcns = {'removeconstantrows','mapminmax'};

%Initilization Functions
FIT1.layers{1}.initFcn = 'initnw';
FIT1.layers{2}.initFcn = 'initnw';
FIT1.layers{3}.initFcn = 'initnw';

%Net Input Functions
FIT1.layers{1}.netInputFcn = 'netsum';
FIT1.layers{2}.netInputFcn = 'netsum';
FIT1.layers{3}.netInputFcn = 'netsum';

%Transfer functions
FIT1.layers{1}.transferFcn = 'satlin';
FIT1.layers{2}.transferFcn = 'purelin';
FIT1.layers{3}.transferFcn = 'purelin';

%Input Weights delays
FIT1.inputWeights{2,1}.delays=0;
FIT1.inputWeights{3,1}.delays=0;

%Input Weights learning
FIT1.inputWeights{1,1}.learn=1;
FIT1.inputWeights{2,1}.learn=1;
FIT1.inputWeights{3,1}.learn=1;
FIT1.inputWeights{1,1}.learnFcn='learncon';
FIT1.inputWeights{2,1}.learnFcn='learncon';
FIT1.inputWeights{3,1}.learnFcn='learncon';

%Layer Weight Functions
FIT1.layerWeights{1,2}.weightFcn='normprod';
FIT1.layerWeights{1,3}.weightFcn='normprod';
FIT1.layerWeights{2,3}.weightFcn='normprod';
;
%Layer Initialization Functions
%FIT1.layerWeights{1,2}.initFcn='initcon';
%FIT1.layerWeights{1,3}.weightFcn='normprod';
%FIT1.layerWeights{2,3}.weightFcn='normprod';

%view(FIT1)

% Setup Division of Data for Training, Validation, Testing
% For a list of all data division functions type: help nndivide
FIT1.divideFcn = 'dividerand';  % Divide data randomly
FIT1.divideMode = 'sample';  % Divide up every sample
FIT1.divideParam.trainRatio = 64/100;
FIT1.divideParam.testRatio = 16/100;
FIT1.divideParam.valRatio = 20/100;

% For help on training function 'trainlm' type: help trainlm
% For a list of all training functions type: help nntrain
FIT1.trainFcn = 'trainrp';  % Resilient Backpropagation
%FIT1.trainFcn = 'trainlm';  % Levenberg-Marquardt
%FIT1.trainFcn = 'trainscg';  % Scaled Conjugate Gradient
%FIT1.trainFcn = 'trainbr';  % Bayesian Regularization
%FIT1.trainFcn = 'traingdm';  % Gradient descent with momentum backpropagation
%FIT1.trainFcn = 'trainb';  % Batch training
%FIT1.trainFcn = 'trainbfg';  % BFGS quasi-Newton backpropagation
%FIT1.trainFcn = 'traincgb';  % Conjugate gradient backpropagation with Powell-Beale restarts
%FIT1.trainFcn = 'trainoss';  % One-step secant backpropagation
%FIT1.trainFcn = 'trainr';  % Random order incremental training with learning functions
%FIT1.trainFcn = 'trains';  % Sequential order incremental training with learning functions

%Training Parameters
FIT1.trainParam.epochs=1000;
FIT1.trainParam.time=Inf;
FIT1.trainParam.min_grad=0.00001;
FIT1.trainParam.max_fail=6;
FIT1.trainParam.delta0=0.07;
FIT1.trainParam.delta_inc=1.25;
FIT1.trainParam.delta_dec=0.5;
FIT1.trainParam.deltamax=50;

% Choose a Performance Function
% For a list of all performance functions type: help nnperformance
FIT1.performFcn = 'mse';  % Mean squared error

% Choose Plot Functions
% For a list of all plot functions type: help nnplot
FIT1.plotFcns = {'plotperform','plottrainstate','ploterrhist', ...
  'plotregression', 'plotfit'};

% Train the Network
[FIT1,tr] = train(FIT1,inputs,targets);

% Test the Network
outputs = FIT1(inputs);
%Outputs >0
for i=1:size(Mnt2old)
   if outputs(1,i) <0
       outputs(1,i)=0.001;
   end
end
errors = gsubtract(targets,outputs);
performance = perform(FIT1,targets,outputs)

Rtr=corrcoef(outputs,Mnt2old);
R2tr=Rtr(1,2)^2

for i=1:max(size(errors))
    errors2(1,i)=errors(1,i)^2;
end
RMSEtr= (mse(errors,outputs))^0.5;

MSEtr=(sum(errors2))/max(size(Mnt2old));
RMSEtr2=MSEtr^0.5;
old=max(size(Mnt2old));
Mtrain=mean(Mnt2old);
Mquadrerrtrain=RMSEtr/(max(size(Mnt2old))^(0.5));
EpctMquad=100*Mquadrerrtrain/Mtrain
Maritmerrtrain=mean(abs(errors));
EpctMaritm=100*Maritmerrtrain/Mtrain
EpctRMSE=100+RMSEtr/Mtrain
PeaksErrratioT=EpctRMSE/EpctMaritm

% Recalculate Training, Validation and Test Performance
trainTargets = targets .* tr.trainMask{1};
%valTargets = targets  .* tr.valMask{1};
%testTargets = targets  .* tr.testMask{1};
trainPerformance = perform(FIT1,trainTargets,outputs);
%valPerformance = perform(FF1,valTargets,outputs)
%testPerformance = perform(FF1,testTargets,outputs)

% View the Network
%view(FF1)

% Plots
% Uncomment these lines to enable various plots.
%figure, plotperform(tr)
%figure, plottrainstate(tr)
%figure, plotfit(net,inputs,targets)
%figure, plotregression(targets,outputs)
%figure, ploterrhist(errors)

%Validation
Outputval=FIT1(Inputs72011');
for i=1:size(Mnt22011)
   if Outputval(1,i) <0
       Outputval(1,i)=0.001;
   end

end
plot (Outputval,'r')
hold on
plot (Mnt22011,'g')
hold off
Rval = corrcoef(Outputval,Mnt22011);
R2val=Rval(1,2)^2
errval=(Outputval-Mnt22011');
for i=1:max(size(errval))
    errval2(1,i)=errval(1,i)^2;
end
RMSEval= (mse(errval,Outputval))^0.5;
MSEval=(sum(errval2))/max(size(Mnt22011));
new=max(size(Mnt22011));
Mval=mean(Mnt22011);
Mquadrerrval=RMSEval/(max(size(Mnt22011))^(0.5));
EpcvMquad=100*Mquadrerrval/Mval
Maritmerrval=mean(abs(errval));
EpcvMaritm=100*Maritmerrval/Mval
EpcvRMSE=100*RMSEval/Mval
PeaksErrratioV=EpcvRMSE/EpcvMaritm_

Basically, at the moment it is just a basic code, where I have highlighted all the possible options available. The data I used for training it are data for the period 2000/2008, and then i use a separate validation set related to six months in 2011. In the last part I created some error indexes.

 

I have to say that I am very new to the NN world, therefore I still miss some theoretical concepts behind, probably. But, with trial and error, I have already tried to improve it in several ways (as you can see from the options I have highlighted) with bad results; only changing the training algorithm I have obtained fairy different results, but usually they are far different from training to training..I always got completely different charts. Would be enough to train it many times and to save the weights of the trial which gave the lowest error?

So, considering that in my validation set, but also in my training set, I have a very low performance (say err = +- 100%), and I don't think I can go to very low values (say +-5%) only with more data available, what can I do, froma network point of view, to improve it? I also tried a feedforward multilayer network with similar results, and a general regression model that gives me very flat results (see code below)

_ GRNN=newgrnn(Inputs7old',Mnt2old') ytr=GRNN(Inputs7old'); figure1=plot (ytr,'g') hold on figure1=plot(Mnt2old,'r') hold off Rtr=corrcoef(Mnt2old,ytr); msetr=mse(GRNN,Mnt2old,ytr');

 

errors = gsubtract(Mnt2old',ytr);
R2tr=Rtr(1,2)^2

for i=1:max(size(errors))
    errors2(1,i)=errors(1,i)^2;
end
RMSEtr= (mse(errors,ytr))^0.5;
MSEtr=(sum(errors2))/max(size(Mnt2old));
old=max(size(Mnt2old));
Mtrain=mean(Mnt2old);
Mquadrerrtrain=RMSEtr*(max(size(Mnt2old))^(-0.5));
EpctRMSE=100*RMSEtr/Mtrain
EpctMquad=100*Mquadrerrtrain/Mtrain
Maritmerrt=mean(abs(errors));
EpctMaritm=100*Maritmerrt/Mtrain
PeaksErrRatioT=EpctRMSE/EpctMaritm

yval=GRNN(Inputs72011');
figure2=plot(yval,'b');
hold on
plot(Mnt22011,'g')
hold off

Rval = corrcoef(yval,Mnt22011);
R2val=Rval(1,2)^2
errval=(yval-Mnt22011');
for i=1:max(size(errval))
    errval2(1,i)=errval(1,i)^2;
end
RMSEval= (mse(errval,yval))^0.5;
MSEval=(sum(errval2))/max(size(Mnt22011));
new=max(size(Mnt22011));
Mval=mean(Mnt22011);
Merrvalquadr=RMSEval/(max(size(Mnt22011))^(0.5));
EpcvMquadr=100*Merrvalquadr/Mval;
Merrvalaritm=mean(abs(errval));
EpcvMaritm=100*Merrvalaritm/Mval
EpcvRMSE=100*RMSEval/Mval
PeaksErrRatioV=EpcvRMSE/EpcvMaritm_

 

ANSWER

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You seem to be wasting a lot of time and space writing code that is unnecessary because you do not rely on defaults. My experience is that 1 hidden layer is sufficient. Given the size of the input and target matrices,( [ I N ] and [ O N ], respectively), the only things that have to be specified are

 

1. The number of input and/or feedback delays in time-series prediction.

 

2. The candidates for number of hidden nodes (e.g., H = 0:10)

 

3. The number of random weight initializations for each H candidate (e.g., Ntrials = 10).

 

4. A nonzero MSE training goal to mitigate overfitting. I favor

 

%net.trainParam.goal = 0.01*Ntrneq*var(T,0,2)/(Neq-Nw) ;

 

CORRECTION:

net.trainParam.goal = 0.01*max(Ndof,0)*var(T,0,2)/Ntrneq

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