I would like to solve an unbounded problem in PDE format by NeuralPDE.
The domains of the problem is x belong [0;inf) and y belong real number (R)
please help me on how could I implement these domains in Julia and whether NeuralPDE could solve the unbounded PDE?
In the case if my boundary condition is x = A if x <= 10 and x = 0 otherwise.
How could I implement the boundary condition like this?
Thank you for your time.
What have you tried so far?
I don’t know if/how NeuralPDE can handle this, but it is possible to define open intervals in DomainSets/ModelingToolkit with Inf as the boundary:
Interval(0, Inf)
Interval(-Inf, Inf)
Another option might be to transform the variables first by some nonlinear transformation that maps the infinite domain to a finite one, e.g. some sigmoidal function (it will probably depend a lot on the actual problem/equations).
Try doing transformations similar to:
https://docs.sciml.ai/Integrals/stable/tutorials/numerical_integrals/#Infinity-handling
Thank you for your information. Your information is helpful to me for the unbounded PDE.
I also had another questions, if the boundary condition in my problem following:
x = A, if x <= 10
x = B, otherwise.
Did you have any experiences to implement it on Neural PDE?
Thank you for your information.
I also had another questions, if the boundary condition in my problem following:
x = A, if x <= 10
x = B, otherwise.
Did you have any experiences to implement it on Neural PDE?
I don’t quite understand.
These are not boundary conditions of a PDE as far as I can tell. What is the state variable? (some function f(x,y) ? )
Boundary conditions are usually conditions on the state variable or its derivative at the boundaries of the system. Something like f(x=0, y) = ... or (df/dx)(x=0, y) = ...
I am sorry for unclear question.
the PDE of f(t, x, y) for t belong (0,T), x belong (0;inf), y belong (-inf, inf)
the boundary is that:
f(T, x, y) = A (constant) if x <= 10
f(T, x, y) = B (constant) if x > 10