How can I specify custom data and a custom loss function?

Hi,

I would like to program a physics-informed neural network (I have attached the paper introducing them). It can be used to solve partial differential equations with given initial and boundary data. Therefore, I need to do two things:

1. I have to manually generate the input data. In Matlab it is very easy, e.g. x = linspace(0, 1, 100). How can I transfer that data as training data to the neural net?

2. I have to manually specify a loss function. More specifically, the loss function is the differential equation and the initial/boundary conditions.

So, I would like to solve the steady-state heat-diffusion equation: d^2T/dx^2 = 5 with T(0) = 0 and T(1) = 3

How can I program this into Matlab?

Answer 1

[Anshika Chaurasia]

Hi Marius,

It is my understanding that input data is defined manually in form of vector.

1. Suppose input data x = linspace(0,1,100). Use following to train network:

x = linspace(0,1,100);
net = train(net,x,t);

Refer to train documentation for training a neural network with user defined training data.

2. Define custom loss function in following way:

loss = CustomLoss(Y,T);%where Y is the network predictions, T are the targets, 
% and loss is the returned loss.

Refer to specify loss function and GAN loss example documentations for specifying custom loss functions.