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

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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 , ,..., , ?
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Ben
Ben on 9 Apr 2024
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.

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Answers (1)

Jayanti
Jayanti on 3 Oct 2024
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:
Hope this helps!

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