Neural network construction where different outputs have different dependencies on the inputs

I want to construct a neural network for a system which is described by the image below. The arrows in the images shows the dependencies of the variables in the system (e.g., is dependent on ). I have two inputs and and outputs and , ,..., , . Three intermediate variables , and connect the inputs and outputs together, while the outputs , ,..., , have dependencies sequentially and is dependent on all the . How can I construct a neural network where the inputs are and and the outputs are and , ,..., , ?

[Ben]

The diagram suggests depends on and depend on (via ). Could you clarify how the simultaneous dependency should be handled?

One way might be a recurrent style network - all the variables are actually time series, and depends on , while depend on . You would hook up a neural network with the and as outputs and write code to feed the back into the network at the next time step.

Answer 1

[Jayanti]

Hi Xuming,

You can start by defining all the layer component with appropriate size. Let’s assume you have input layer of size 10 (you can choose according to your requirement).

x_A = featureInputLayer(10, 'Name', 'x_a');

Similarly, you can create another input layer .

Now you can create intermediate layer of (suppose) size=20.

I_1 = fullyConnectedLayer(20, 'Name', 'I_1');

Similarly create other two layers and .

For explanation, I am assuming n=3 that is we have three layers which is referred as , and . You can extend this to any value of n. Below code will create layer with size=10.

y_B1 = fullyConnectedLayer(10, 'Name', 'y_b1');

Similarly define for other layers like and , .

Now you need to connect all the layers according to your need. I am attaching the code for your reference.

layers = connectLayers(layers, 'x_a', 'I_1'); 
layers = connectLayers(layers, 'I_1', 'I_2'); 
layers = connectLayers(layers, 'I_2', 'I_3'); 

layers = connectLayers(layers, 'x_b', 'y_b1');
layers = connectLayers(layers, 'x_b', 'y_b2'); 
layers = connectLayers(layers, 'x_b', 'y_b3');

layers = connectLayers(layers, 'I_3', 'y_b1'); 

layers = connectLayers(layers, 'y_b1', 'y_a/in1'); 
layers = connectLayers(layers, 'y_b2', 'y_a/in2'); 
layers = connectLayers(layers, 'y_b3', 'y_a/in3'); 

layers = connectLayers(layers, 'y_a', 'I_3');

Also I am attaching the documentation link for various layers for your reference:

https://www.mathworks.com/help/deeplearning/ref/nnet.cnn.layer.featureinputlayer.html

https://www.mathworks.com/help/deeplearning/ref/nnet.cnn.layer.fullyconnectedlayer.html

https://www.mathworks.com/help/deeplearning/ref/nnet.cnn.layergraph.connectlayers.html

Hope this helps!