What is the criteria behind choosing number of neurons and layers in this MATLAB example? "Solve Partial Differential Equation with LBFGS Method and Deep Learning"
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Muhammad Mahmoud
on 27 Apr 2023
Commented: Muhammad Mahmoud
on 14 May 2023
The number of layers and neurons in this example, "Solve Partial Differential Equation with LBFGS Method and Deep Learning," are set to 9 and 20, respectively.
Which criteria would be used to select these numbers? then why?
Thanks in advance.
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Ranjeet
on 12 May 2023
The example given refers to the work Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations.
The work starts by taking 9 hidden layers and 20 neurons in each. This should be the motivation behind taking the same network architecture and experiment.
However, Table 2 on page 9 in the above article shows experimentation with different number of layers and neurons as well. It is clear from the table that taking a greater number of layers and neurons have decreased the error metric. Taking 9 hidden layers and 20 neurons is a good trade-off between accuracy and network size.
Following is the part 2 of the work, it can be referred for more in-depth analysis -
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