Icy or rocky? Convective or stable?

We present a new framework for constructing agnostic and yet physical models for planetary interiors and apply it to Uranus and Neptune. Unlike previous research that either impose rigid assumptions or rely on simplified empirical profiles, our approach bridges both paradigms. Starting from randomly generated density profiles, we applied an iterative algorithm that converges towards models that simultaneously satisfy hydrostatic equilibrium, match the observed gravitational moments, and remain thermodynamically and compositionally consistent. The inferred interior models for Uranus and Neptune span a wide range of possible interior structures, in particular encompassing both water-dominated and rock-dominated configurations (rock-to-water mass ratios between 0.04–3.92 for Uranus and 0.20–1.78 for Neptune). All models contain convective regions with ionic water and have temperature–pressure profiles that remain above the demixing curves for hydrogen–helium–water mixtures. This offers both a plausible explanation for the observed non-dipolar magnetic fields and indicates that no hydrogen–helium–water demixing occurs. We find a higher H-He mass fraction in the outer-most convection zones for Uranus (0.62–0.73) compared to Neptune (0.25–0.49) and that Uranus’ magnetic field is likely generated deeper in the interior compared to Neptune. We infer upper limits of 0.69–0.74 (Uranus) versus 0.78–0.92 (Neptune) for the outer edges of the dynamo regions in units of normalised radii. Overall, our findings challenge the conventional classification of Uranus and Neptune as ’ice giants’ and underscore the need for improved observational data or formation constraints to break compositional degeneracy.