SymPy size error and Setting 2D point constraints

[caio.leao]

I’m trying to implement this PDE class and I’m having some difficulties, am I doing something wrong?

At the PointwiseInteriorConstraint I get the error: ValueError: C order implies last dim (1) == len(args) (2)

error:

I need the initial condition T(4,1) = 0 and I am not successful

how the network was set

I would be grateful if someone could help me.

[ngeneva]

Hi @caio.leao

I’m not sure what is causing that error you’re getting. I was not able to reproduce it on my end. However there are a few issues. The first is that the Rectangle geometry object returns x,y, so your ‘z’ variable in your PDE and model won’t be provided. This would cause a graph unrolling error. The fix is simply changing z to y.

The second issue is that in your PointwiseInteriorConstraint you don’t provide a v variable which will also cause a graph unrolling error. Your PDE can’t be calculated without it. To fix this I added v as a parameterized variable.

I created a simple script to test on my end and seems it works fine on my end:

class Eikonal(PDE):
    name = "Eikonal"
    def __init__(self, T="T", v="v"):
        self.T = T
        x, y = Symbol('x'), Symbol('y')
        input_variables = {"x": x, "y": y}
        T = Function(T)(*input_variables)
        v = Function(v)(*input_variables)

        self.equations = {}
        self.equations['Eikonal'] = ((T.diff(x))**2 + (T.diff(y))**2 + (1/v)**2)
       
@modulus.sym.main(config_path="conf", config_name="config")
def run(cfg: ModulusConfig) -> None:
    # make list of nodes to unroll graph on
    pde = Eikonal( T="T", v="v")
    model = instantiate_arch(
        input_keys=[Key("x"), Key("y")],
        output_keys=[Key("T")],
        cfg=cfg.arch.fully_connected,
    )
    nodes = pde.make_nodes() + [model.make_node(name="my_network")]

    dLen = 6
    rec = Rectangle((0,0), (dLen, dLen))
    # add constraints to solver
    # make geometry
    x, y = Symbol("x"), Symbol("y")
    v = Symbol("v")

    interior = PointwiseInteriorConstraint(
        nodes=nodes,
        geometry=rec,
        outvar={"Eikonal": 0},
        batch_size=128,
        parameterization={v: 0}
    )
   # ..... more code here
    
if __name__ == "__main__":
    run()

[caio.leao]

@ngeneva

Dear @ngenevam I’m really grateful for help me with the code, now it is working. However, I would like to ask for another question. Looking in the documentation, I can’t find a good way to make a point restriction on data in two dimensions of two dimensions. I mean, in this case I need T(x,y) to be like this T(4,1) = (0,0). I looked at the criteria but it refers to boundary conditions my problem has no border. I tried this way but I was not successful,

font = PointwiseInteriorConstraint(
     nodes = nodes,
     geometry = rec, 
     outvar={"T":0.0},
     batch_size = 1, 
     parameterization= {x:1 , y:4 },
     
     )
domain.add_constraint(font,"font_position") 

or more easy T = 0 for v = 0 using PointwiseConstraint.from_numpy
Could you help me with this?

[ngeneva]

Hi @caio.leao

Yes, unfortunately we don’t have a 2D point primitive as far as I know. You could try a few things.

1. Define the input/ output training points for this constraint manually via numpy dictionaries. (See this thread and embedded links). This is probably what I would recommend the most.

2. Use the criteria to create a small bounding box around the point of interest.

3. A hacky approach would be to use a 1D point geometry for the x dimension and then parameterize the y variable like what you have here.

4. Another option I would try is to create a 2D circle geometry with a really small radius so its approximately a point.

[caio.leao]

@ngeneva

Thanks. I was able to run successfully after the previous suggestion using PointwiseConstraint.from_numpy. I’ll try the other two suggestions as I need to vary this initial condition. A suggestion for Nvidia is to generate the direct possibility of entering these point restriction conditions