What does determine width of output layer?

[aoguedao]

Hi again!

I know this question could seem a little bit naïve because for a simple example as this from the demos is clear it is a 2-dimensional system of equations then net has two elements in the output layer.

On the other hand, inverse Poisson equation demo is an unidimensional PDE and, even there is just one Hessian in the function pde and this one just returns a single element. however, the output layer also have two elements. I know this is for learning $u(x)$ and $q(x)$, but I don't understand how was defined in the dde.model that it need to learn two things ($u$ and $q$). Is it related to the dimension of the observed data?

Thanks in advance for your help.

[forxltk]

The pde function returns the pde loss, but not the outputs of the NN.

In the inverse Poisson case, u(x) and q(x) are unknown that we need to predict both of them. So there are two outputs of the NN, one is u(x), another is q(x). But u(x) and q(x) only follow one governing equation ddu=q(x), which is the return of pde function.

[aoguedao]

Hi @forxltk! Thanks for your answer. I do understand the problem statement but I haven't been able to understand how (programmatically) DeepXDE knows what to learn. Documentation says "The second argument is the network output, i.e., the solution u, q" but function pde doesn't declare the size of y, it just unpacking it in the first line.

My apologies if it is a really dumb question.

[forxltk]

OK, the size of y is defined in the NN configuration.
net = dde.nn.PFNN([1, [20, 20], [20, 20], [20, 20], 2], "tanh", "Glorot uniform")
Here 1 is the size of x, [20, 20] is the size of hidden layers, and 2 is the size of y.

[aoguedao]

Thank you! Just for clarifying, let's suppose I want to add another unknown function. Should I modify the function pde unpacking as u, q, p = y[:, 0:1], y[:, 1:2], y[:, 1:2] and then just change the network architecture?? For example net = dde.nn.PFNN([1, [20, 20, 20], [20, 20, 20], [20, 20, 20], 3], "tanh", "Glorot uniform"), right?

[forxltk]

Yes