Data-Driven Constitutive Relation Reveals Scaling Law for Hydrodynamic Transport Coefficients
This work addresses the problem of extending hydrodynamics equations for physicists and engineers, though it is incremental as it builds on existing data-driven approaches with theoretical justification.
The authors tackled the challenge of deriving accurate constitutive relations for hydrodynamic transport across gas density regimes by proposing a data-driven model based on scaling laws, which outperformed traditional methods like Chapman-Enskog expansion and moment methods in Rayleigh scattering spectra calculations.
Finding extended hydrodynamics equations valid from the dense gas region to the rarefied gas region remains a great challenge. The key to success is to obtain accurate constitutive relations for stress and heat flux. Data-driven models offer a new phenomenological approach to learning constitutive relations from data. Such models enable complex constitutive relations that extend Newton's law of viscosity and Fourier's law of heat conduction by regression on higher derivatives. However, the choices of derivatives in these models are ad-hoc without a clear physical explanation. We investigated data-driven models theoretically on a linear system. We argue that these models are equivalent to non-linear length scale scaling laws of transport coefficients. The equivalence to scaling laws justified the physical plausibility and revealed the limitation of data-driven models. Our argument also points out that modeling the scaling law could avoid practical difficulties in data-driven models like derivative estimation and variable selection on noisy data. We further proposed a constitutive relation model based on scaling law and tested it on the calculation of Rayleigh scattering spectra. The result shows our data-driven model has a clear advantage over the Chapman-Enskog expansion and moment methods.