Infrared Fixed Points of Cosmological Density Fields from a Neural Operator Approach to the Functional Renormalization Group

We present a neural operator that solves the Wetterich equation as a hard constraint to learn the effective action Γ_k[δ] of cosmological density fields from N-body simulations. Derivative expansion coefficients U_k(δ), Z_k(δ), Y_k(δ) at each renormalization group scale yield all observables by functional differentiation without additional parameters. The network discovers an infrared fixed point at k* ≈ 0.03 h Mpc^-1 with correlation dimension D_2 = 1.73 ± 0.08. Against Quijote and AbacusSummit suites, the power spectrum achieves ΔP(k)/P(k) < 1% for k < 1 h Mpc^-1.