How to train NARX neural network in closed loop

 I am am trying to use the neural network toolbox to predict an internal temperature given a number of input conditions. I have used an automatically generated code for a NARX network and made some small changes. I am aware that the typical workflow is to train open and then change to closed, however I would like to compare the results from this approach with training the network initially in closed form.

 

When training with the fourth input arguement of narxnet command set to 'open' the network trained with no problems. When I change this to 'closed' I am getting the following error messages:

 

 

Error using network/subsasgn>network_subsasgn (line 91)
Index exceeds matrix dimensions.

Error in network/subsasgn (line 13)
net = network_subsasgn(net,subscripts,v,netname);

Error in narx_closed (line 28)
net.inputs{2}.processFcns =
{'removeconstantrows','mapminmax'};

I'm not really sure what the problem is as the Neural Network Toolbox Users Guide seems to suggest that this is all you need to do to create a closed loop NARX network and train the network directly. I have included my full code below:

 

 

%%Closed Loop NARX Neural Network

%%Load data and create input and output matrices

load('junior_class_data.mat');
U = [Outdoor_Temp, Position, Wind_Speed, Wind_Direction];
Y = [Zone_Temp];

inputSeries = tonndata(U,false,false);
targetSeries = tonndata(Y,false,false);

%%Create a Nonlinear Autoregressive Network with External Input

inputDelays = 0:2;
feedbackDelays = 1:2;
hiddenLayerSize = 10;
net = narxnet(inputDelays,feedbackDelays,hiddenLayerSize,'closed');

%%Pre-Processing

% Choose Input and Feedback Pre/Post-Processing Functions
% Settings for feedback input are automatically applied to feedback output
% For a list of all processing functions type: help nnprocess
% Customize input parameters at: net.inputs{i}.processParam
% Customize output parameters at: net.outputs{i}.processParam
net.inputs{1}.processFcns = {'removeconstantrows','mapminmax'};
net.inputs{2}.processFcns = {'removeconstantrows','mapminmax'};

% Prepare the Data for Training and Simulation
% The function PREPARETS prepares timeseries data for a particular network,
% shifting time by the minimum amount to fill input states and layer states.
% Using PREPARETS allows you to keep your original time series data unchanged, while
% easily customizing it for networks with differing numbers of delays, with
% open loop or closed loop feedback modes.
[inputs,inputStates,layerStates,targets] = preparets(net,inputSeries,{},targetSeries);

% Setup Division of Data for Training, Validation, Testing
% For a list of all data division functions type: help nndivide
net.divideFcn = 'divideblock';
% The property DIVIDEMODE set to TIMESTEP means that targets are divided
% into training, validation and test sets according to timesteps.
% For a list of data division modes type: help nntype_data_division_mode
net.divideMode = 'value';  % Divide up every value
net.divideParam.trainRatio = 80/100;
net.divideParam.valRatio = 15/100;
net.divideParam.testRatio = 5/100;

%%Training Function
% For a list of all training functions type: help nntrain
% Customize training parameters at: net.trainParam
net.trainFcn = 'trainlm';  % Levenberg-Marquardt

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

% Choose Plot Functions
% For a list of all plot functions type: help nnplot
% Customize plot parameters at: net.plotParam
net.plotFcns = {'plotperform','plottrainstate','plotresponse', ...
  'ploterrcorr', 'plotinerrcorr'};

%%Train the Network
[net,tr] = train(net,inputs,targets,inputStates,layerStates);

%%Test the Network
outputs = net(inputs,inputStates,layerStates);
errors = gsubtract(targets,outputs);
performance = perform(net,targets,outputs)

% Recalculate Training, Validation and Test Performance
trainTargets = gmultiply(targets,tr.trainMask);
valTargets = gmultiply(targets,tr.valMask);
testTargets = gmultiply(targets,tr.testMask);
trainPerformance = perform(net,trainTargets,outputs)
valPerformance = perform(net,valTargets,outputs)
testPerformance = perform(net,testTargets,outputs)

%%View the Network
view(net)

ANSWER

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 close all, clear all, clc
disp('DIRECT TRAINING OF A CLOSELOOP NARXNET')
load('maglev_dataset');
whos
%   Name              Size      Bytes   Class 
%   maglevInputs      1x4001    272068  cell                
%   maglevTargets     1x4001    272068  cell                
X   = maglevInputs; 
T   = maglevTargets;
ID  = 1:2, FD = 1:2, H  = 10   % Default values
netc                    = closeloop(narxnet(ID,FD,H));
view(netc)
netc.divideFcn          = 'divideblock';
[ Xcs, Xci, Aci, Tcs ]  = preparets( netc, X, {}, T );
tcs                     = cell2mat(Tcs);
whos X T Xcs Xci Aci Tcs tcs
%  Name     Size     Bytes   Class
%   Aci     2x2         416  cell                
%   T       1x4001   272068  cell                
%   Tcs     1x3999   271932  cell                
%   X       1x4001   272068  cell                
%   Xci     1x2         136  cell                
%   Xcs     1x3999   271932  cell                
%   tcs     1x3999    31992  double              

 MSE00cs = var(tcs,1)  % 2.0021 ( 1-dim MSE reference)

 rng(4151941)
tic
[netc trc Ycs Ecs Xcf Acf ] = train(netc,Xcs,Tcs,Xci,Aci);
toc                           % 197 sec
view(netc)
whos Ycs Ecs Xcf Acf
%   Name    Size     Bytes     Class
%   Acf     2x2         416    cell               
%   Ecs     1x3999   271932    cell               
%   Xcf     1x2         136    cell               
%   Ycs     1x3999   271932    cell               

 stopcriterion  = trc.stop                    % Validation stop
bestepoch      = trc.best_epoch               % 4
ecs            = cell2mat(Ecs);
NMSEcs         = mse(ecs)/MSE00cs             %  1.2843
tcstrn         = tcs(trc.trainInd);
tcsval         = tcs(trc.valInd);
tcstst         = tcs(trc.testInd);
NMSEcstrn      = trc.best_perf/var(tcstrn,1)  %  1.3495
NMSEcsval      = trc.best_vperf/var(tcsval,1) %  0.9325
NMSEcstst      = trc.best_tperf/var(tcstst,1) %  1.6109

I consider a good design to have a normalized MSE,

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