How to generate a fixed uniform training samples using PointwiseInteriorConstraint

[SinaAkhyani]

Is it possible to generate a fixed uniform spatio-temporal ((x, t)) mesh using the PointwiseInteriorConstraint class for multiple time steps to have a full control on the training mesh?

I tried the following approach:

geo = Line1D(0, 10)
time_range_interior = np.linspace(1, 20, 100)

for j, time_val in enumerate(time_range_interior):
interior = PointwiseInteriorConstraint(
nodes=nodes,
geometry=geo,
outvar={"lmxs": 0, "lmxf": 0},
batch_size=cfg.batch_size.interior,
lambda_weighting={"lmxs": 1, "lmxf": 1},
parameterization={t_symbol: time_val},
fixed_dataset=True,
quasirandom=True,
)
domain.add_constraint(interior, f"interior_t{j}")

According to the above code, for each "time_val", different spatial points (x) are sampled from "geo". However, my goal is to use the same fixed set of spatial samples for all "interior_t{j}"s constraints.

I would appreciate your advice on this.

[SinaAkhyani]

I figured it out by using the PointwiseConstraint class and .from_numpy() method. Full description of the arguments can be found in physicsnemo.sym.domain.constraint.PointwiseConstraint.

[ktangsali]

Yes, for fully deterministic sampling, you can pre-compute the point cloud and use the from_numpy() method.