A Physics-First Hamiltonian Latent Model for Twelve Universality Classes of Fluid Behaviour
Abstract
Abstract We present Fluido Universal (FU), a physics-first, purely analytic reduced-order framework that reproduces eighteen universal indicators of fluid behaviour across twelve distinct physical regimes—from wall-bounded turbulence to superfluid helium, from rarefied Martian CO2 to solar-wind plasma. Unlike data-driven closures (e.g. graph neural networks, WMLES with embedded ML, PINNs), FU contains no learned parameters, no autoencoder, and no sparseregression step: every indicator is either a closed-form algebraic law or a first-principles ODE integrated by a fourth-order Runge–Kutta scheme, using only CODATA 2022 constants. The framework is embedded in an interactive WebGL2 Navier–Stokes solver that runs on consumer hardware and validates all eighteen indicators live. The eighteen indicators are organised in two tiers: Tier I (Indicators 01–12) are algebraic universal laws whose verification is independent of the lattice, while Tier II (Indicators 13–18) are canonical three-dimensional turbulence identities evaluated from sampled vorticity and spectra. The mean absolute percentage error (MAPE) is 0.94 % with maximum 3.10 % across the eighteen indicators, versus a 6 % to 18 % range for industrial LES and 2 % to 7 % for reference DNS at comparable resolution. Crucially, the reference values are algebraic expressions evaluated at the same physical parameters, not DNS time series; the MAPE therefore quantifies algebraic closure fidelity, not discretisation error or…
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