You have correctly understood how the main part of the neural network works, however, the inputs and outputs of the neural network are also doing some processing.
You can see the processing functions and settings in the processFcns and processSettings fields of inputs and the second layer's outputs:
net.inputs{1}.processFcns
net.inputs{1}.processSettings
net.outputs{2}.processFcns
net.outputs{2}.processSettings
The processSettings were automatically set upon first training the network. For instance the processing MAPMINMAX's settings save the range of inputs X so it can consistently map inputs into the range [-1 1].
Type "help nnprocess" to see a list of processing functions you can assign to a network before training if you like, beyond the ones your network might have.
If the first processing function for inputs is MAPMINMAX then you can process the inputs as follows:
x = 0; for i=1:numel(net.inputs{1}.processFcns) x = feval(net.inputs{1}.processFcns{i},x,net.inputs{i}.processSettings); end
At this point you can put X into your network equation above to calculate Y. Here is another notation for that calculation. BSXFUN makes it easy to add bias vectors to weighted matrices.
y = bsxfun(@plus,net.LW{2,1}*bsxfun(@plus,tansig(net1.IW{1,1}*x,net.b{1}),net.b{2})
Then reverse process the output Y:
for i=numel(net.outputs{2}.processFcns):-1:1 y = feval(net.outputs{2}.processFcns{i},'reverse',y,net.outputs{2}.processSettings{i}); end
At that point Y should be the same as you got for SIM(NET1,0).
