Learning the Optimal Hydrodynamic Closure

TL;DR

This paper introduces an optimal hydrodynamic model for rarefied gas flows that leverages spectral closure theory and machine learning to accurately derive transport coefficients, outperforming previous models.

Contribution

It combines spectral closure theory with machine learning to derive an optimal hydrodynamic model directly from kinetic data, independent of small Knudsen number assumptions.

Findings

Outperforms previous constitutive laws for higher-order hydrodynamics

Aligns closely with underlying kinetic models, proving optimality

Does not rely on small Knudsen number assumptions

Abstract

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.