Soft routing among process experts helps PDE forecasting, but gains prove seed-dependent
The authors propose COSMOS, a neural operator that densely mixes four process-biased specialists with a learned continuous gate instead of sparse top-K expert selection. On PDEBench families, a locked three-seed run beat a tuned FNO on diffusion-reaction and matched it on Navier-Stokes, but an 11-seed audit showed the diffusion-reaction gain was unstable. Soft routing beat hard top-1 routing by 2.2x in error, yet replacing the learned gate with the generator's true mixture weights further lowered error, and routing labels did not align with physical mechanisms.
