Hi @npstrike
Apologies for the delay. I did take a look at the problem and did notice pretty slow training progress, however the overall problem set up appears good.
Regardless I have a few comments / suggestions I would eventually try on this type of problem which are below. Please correct me if something seems off:
 The first thing that I saw was that the integral continuity planes are positioned at the entrances of the pipe. For example this one here:
integral_continuity = IntegralBoundaryConstraint(
nodes=nodes,
geometry=inlet_branch_integral_mesh,
.....
)
domain.add_constraint(integral_continuity, "integral_continuity_branch")
This is using the inlet mesh of the branch tube which results in an integral continuity plane just at the entrance of the mesh which isn’t actually that beneficial. Ideally we want these integral planes to be spaced out all along this inlet tube where we know the total flow rate. For example in the image below in paraview, the red points are the sampled current integral plane, the green are the volume and purple are where some good integral continuity could be placed.
Ideally you want these to be random and a few per batch. I think you could create a 2D circle primitive with a symbol for its Y location, one can then parameterize the Y variable in the integral continuity to sample circles along the vertical (Y) axis. (I think, havent tried so dont quote me)
Same deal for the other inlet tube (and even the outlet). Setting this up correctly will be likely to make a large difference in convergence.

What Reynolds number is this? I have not done the calculation myself, but if its quite high resolving the boundaries will be very challenging and I would probably recommend adding a zero equation turbulence model to the PDE (example). And also adjusting the sampling so you have a bulk flow constraint and then a near wall constraint. Can use the SDF as a criteria to accomplish this. We have used this in the past for some of the higher Re flows such as the FPGA problem.

I would have to look at the scaling more, but I’m thinking maybe theres some adjustments that could be made there to make the inlet velocities / viscosity with slightly more normalized values while maintaining the Reynolds number. Perhaps its alright as is.

Make sure you are not making the pipe diameter too small for the sake of decreasing the lengths of the tubes. If you know the inlet is likely laminar, you could decrease the length of the inlet pipes to make the diameter of the pipes larger since you know the flow profile (v(r) = v_0 (1  r^2 / R^2) or something like that, cant recall exactly please check).

Consider using a fourier net model (keyword
fourier
in the config for the model, docs are incorrect currently). They can work better for these problems with different length scales (in your case a long tube length but small diameter)
Unfortunately, I dont have bandwidth at this very moment to dig into this problem more. Although I do intend to keep it on my radar for the future. Maybe trying out some of these suggestions. Naturally there’s a number of things that could be tinkered with but the first priority is to get the flow to converge consistency (even at a slightly different Reynolds number although your validation will be useless).