How to choose the inputs and outputs of branch net and trunk net?

[LearnTo168Learn]

Hi, thank you for your nice work and code!
I have a few questions about the code.

1. In your PI_DeepONet_pendulum.ipynb，the input of branch net is u_train, the input of trunk net is y_train, and the final output is s_train, i am a little confused about how to choose the input and output. It seems that no supervised information about IC or boundary condition is needed!

u_train = random.uniform(key_u, (m,2), minval=-3, maxval=3)
y_train = np.zeros((P,))
s_train = u_train

2. you have solved forword problems with your PI-DeepOnet, then is it possible to solve inverse problem with your framework ,such as paramter identification？

[sifanexisted]

Hi,

Thank you for your kind works. As for your questions,

A1: Yes, in principle physics-informed DeepONet does not require any observational measurements except for the given and initial conditions. For this particular example you mentioned, u_train is the input parameter representing the initial state of the ODE system and the output is the same as u_train since we aim to fit the initial condition at y = 0. You may check our paper for more details.

A2: My answer is YES! You can use physics-informed deeponet to solve inverse problems and we already had some preliminary results.