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

Question

Xuming Yuan 2024-4-8

0
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回答： Jayanti 2024-10-3

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

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 2024-4-9

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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Answer 1

Jayanti 2024-10-3

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在 MATLAB Online 中打开

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');