am i using the results of the neural network fitting tool correctly?

hello,

i'm relatively new to nn and am not sure if nftool is the right tool to use for this problem.

i have three time series that are are the inputs to a nonlinear system. in a perfect world, the output of this nonlinear system would be a constant time series. here is my attempt to use a neural network to model this nonlinear system (a representative example with noise):

x=linspace(0,199,200);

inputs(1,:)=exp(-x/100)+exp(-x/10)+randn(1,200)/20; % exponential function
inputs(2,:)=exp(-((x-199)/100).^2)+randn(1,200)/50; % Gaussian function
inputs(3,:)=sin(x/2)+randn(1,200)/10;               % sinusoid

target=median(inputs(1,:))*ones(1,200)+randn(1,200)/1000; % constant

net=fitnet(10);
net.inputs{1}.processFcns={'removeconstantrows','mapminmax'};
net.outputs{2}.processFcns={'removeconstantrows','mapminmax'};
net.divideFcn='dividerand';
net.divideMode='sample';
net.divideParam.trainRatio=70/100;
net.divideParam.valRatio=15/100;
net.divideParam.testRatio=15/100;
net.trainFcn='trainlm';
net.performFcn='mse';

[net,tr]=train(net,inputs,target);
output=net(inputs);

the output of this appears to yield a time series similar to the target series within its abilities to make a constant out of the three input time series.

my question comes when i use this trained network on a similar set of inputs, for example if i add a constant to the first input:

inputs(1,:)=inputs(1,:)+10;
output=net(inputs);

i (naively) expected that i would get the same output as before, just shifted by 10 (i.e. what i just added to the first input), however, i get something else altogether.

am i doing something wrong, and/or is there a better way to use neural networks for nonlinear, multidimensional transfer function estimation?

thanks!

Answer 1

[Greg Heath]

The neural network is just a model that characterizes the I/O mapping of the design (train+val) data. If nondesign data doesn't have, approximately, the same summary stats, then don't expect good reslts.

Hope this helps.

Greg