% Solve an Autoregression Problem with External Input with a NARX Neural Network
% Script generated by Neural Time Series app
% Created 11-Apr-2024 12:53:07
%
% This script assumes these variables are defined:
%
% input - input time series.
% output - feedback time series.
X = tonndata(input,false,false);
T = tonndata(output,false,false);
% Choose a Training Function
% For a list of all training functions type: help nntrain
% 'trainlm' is usually fastest.
% 'trainbr' takes longer but may be better for challenging problems.
% 'trainscg' uses less memory. Suitable in low memory situations.
trainFcn = 'trainlm'; % Levenberg-Marquardt backpropagation.
% Create a Nonlinear Autoregressive Network with External Input
inputDelays = 1:4;
feedbackDelays = 1:4;
hiddenLayerSize = 10;
net = narxnet(inputDelays,feedbackDelays,hiddenLayerSize,'open',trainFcn);
% 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.
[x,xi,ai,t] = preparets(net,X,{},T);
% Setup Division of Data for Training, Validation, Testing
% For a list of all data division functions type: help nndivision
net.divideFcn = 'dividerand'; % Divide data randomly
net.divideMode = 'time'; % Divide up every sample
net.divideParam.trainRatio = 80/100;
net.divideParam.valRatio = 5/100;
net.divideParam.testRatio = 15/100;
% Choose a Performance Function
% For a list of all performance functions type: help nnperformance
net.performFcn = 'mse'; % Mean Squared Error
% Choose Plot Functions
% For a list of all plot functions type: help nnplot
net.plotFcns = {'plotperform','plottrainstate', 'ploterrhist', ...
'plotregression', 'plotresponse', 'ploterrcorr', 'plotinerrcorr'};
% Train the Network
[net,tr] = train(net,x,t,xi,ai);
% Test the Network
y = net(x,xi,ai);
e = gsubtract(t,y);
performance = perform(net,t,y)
% Recalculate Training, Validation and Test Performance
trainTargets = gmultiply(t,tr.trainMask);
valTargets = gmultiply(t,tr.valMask);
testTargets = gmultiply(t,tr.testMask);
trainPerformance = perform(net,trainTargets,y)
valPerformance = perform(net,valTargets,y)
testPerformance = perform(net,testTargets,y)
% View the Network
view(net)
% Plots
% Uncomment these lines to enable various plots.
%figure, plotperform(tr)
%figure, plottrainstate(tr)
%figure, ploterrhist(e)
%figure, plotregression(t,y)
%figure, plotresponse(t,y)
%figure, ploterrcorr(e)
%figure, plotinerrcorr(x,e)
% Closed Loop Network
% Use this network to do multi-step prediction.
% The function CLOSELOOP replaces the feedback input with a direct
% connection from the output layer.
netc = closeloop(net);
netc.name = [net.name ' - Closed Loop'];
view(netc)
[xc,xic,aic,tc] = preparets(netc,X,{},T);
yc = netc(xc,xic,aic);
closedLoopPerformance = perform(net,tc,yc)
% Multi-step Prediction
% Sometimes it is useful to simulate a network in open-loop form for as
% long as there is known output data, and then switch to closed-loop form
% to perform multistep prediction while providing only the external input.
% Here all but 5 timesteps of the input series and target series are used
% to simulate the network in open-loop form, taking advantage of the higher
% accuracy that providing the target series produces:
numTimesteps = size(x,2);
knownOutputTimesteps = 1:(numTimesteps-5);
predictOutputTimesteps = (numTimesteps-4):numTimesteps;
X1 = X(:,knownOutputTimesteps);
T1 = T(:,knownOutputTimesteps);
[x1,xio,aio] = preparets(net,X1,{},T1);
[y1,xfo,afo] = net(x1,xio,aio);
% Next the the network and its final states will be converted to
% closed-loop form to make five predictions with only the five inputs
% provided.
x2 = X(1,predictOutputTimesteps);
[netc,xic,aic] = closeloop(net,xfo,afo);
[y2,xfc,afc] = netc(x2,xic,aic);
multiStepPerformance = perform(net,T(1,predictOutputTimesteps),y2)
% Alternate predictions can be made for different values of x2, or further
% predictions can be made by continuing simulation with additional external
% inputs and the last closed-loop states xfc and afc.
% Step-Ahead Prediction Network
% For some applications it helps to get the prediction a timestep early.
% The original network returns predicted y(t+1) at the same time it is
% given y(t+1). For some applications such as decision making, it would
% help to have predicted y(t+1) once y(t) is available, but before the
% actual y(t+1) occurs. The network can be made to return its output a
% timestep early by removing one delay so that its minimal tap delay is now
% 0 instead of 1. The new network returns the same outputs as the original
% network, but outputs are shifted left one timestep.
nets = removedelay(net);
nets.name = [net.name ' - Predict One Step Ahead'];
view(nets)
[xs,xis,ais,ts] = preparets(nets,X,{},T);
ys = nets(xs,xis,ais);
stepAheadPerformance = perform(nets,ts,ys)
% Deployment
% Change the (false) values to (true) to enable the following code blocks.
% See the help for each generation function for more information.
if (false)
% Generate MATLAB function for neural network for application
% deployment in MATLAB scripts or with MATLAB Compiler and Builder
% tools, or simply to examine the calculations your trained neural
% network performs.
genFunction(net,'myNeuralNetworkFunction');
y = myNeuralNetworkFunction(x,xi,ai);
end
if (false)
% Generate a matrix-only MATLAB function for neural network code
% generation with MATLAB Coder tools.
genFunction(net,'myNeuralNetworkFunction','MatrixOnly','yes');
x1 = cell2mat(x(1,:));
x2 = cell2mat(x(2,:));
xi1 = cell2mat(xi(1,:));
xi2 = cell2mat(xi(2,:));
y = myNeuralNetworkFunction(x1,x2,xi1,xi2);
end
if (false)
% Generate a Simulink diagram for simulation or deployment with.
% Simulink Coder tools.
gensim(net);
end
