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"

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.

Answer 1

[Ranjeet]

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.

[Muhammad Mahmoud]

@Ranjeet

Many thanks for your help! I appreciate your assistance. :)