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 2023-4-27

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评论： Muhammad Mahmoud 2023-5-14

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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Answer 1

Ranjeet 2023-5-12

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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 -

Physics Informed Deep Learning (Part II): Data-driven Solutions of Nonlinear Partial Differential Equations.