Learning the Optimal Hydrodynamic Closure

We present the optimal hydrodynamic model for rarefied gas flows relative to a given kinetic model by combining the recent theory of slow spectral closure with machine learning techniques. We learn generalized transport coefficients from density fluctuation data for the Shakhov model as well as Monte Carlo Simulations and demonstrate that our approach decisively outperforms previously proposed constitutive laws for higher-order hydrodynamics. The novel hydrodynamic model is in close alignment with the underlying kinetic models, thus proving the optimality of the slow spectral closure. Our theory is independent on any smallness assumption of the Knudsen number and is formulated solely in terms of macroscopic observables.