DeepOnet with variable IC for ODEs system

[lorenzobranca]

Hi,

I would like some clarification on how to use DeepOnet in a case of ODEs system with variable ICs.

Let's take the following system as example in a time interval t \in [0,1]:

dy1/dt = -y1 + y1*y2

dy2/dt = y2 - y1

with ICs:

y1(0), y2(0) = a, b

where a,b are ours parameters.

I have few questions regarding this:

1. the input of the trunk net: should it be the RHS of the system evaluated in m points (t1,... tm), but now I have two eqs end two parameters (a,b). How to do that?

2. Once trained, to be useful DeepOnet should predict the solution (y1(t), y2(t)) for any Initial Condition (a,b). However the method model.predict() wants the same input that we give in the training phase (the RHS). It confuse me.

I hope someone can clarify my doubts, thanks in advance.