A system of PDE and ODE

General Usage
1

Is PINN capable of solving a time dependent system consisting of a PDE and an ODE?
for example if there is a system like below:

eq = [A * Dt(u1(t,x)) ~ B * Dx(u(t,x)) - C* Dt(u2(t)),
Dt(u2(t)) ~ D * u2(t) * exp(E * u1(t,x))]

For this system would PINN couple solve it or should I put it in iterations and put the u1 and u2 from previous steps into the equation for every new steps?

2

Yup. It may not be as easy to solve as NNODE, which specializes the boundary condition in a nice way, but an ODE is just a 1-dimensional PDE so yeah it’s fine.

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