标题： 数据驱动的本构关系揭示流体动力学输运系数的标度定律 显示英文标题

标题： Data-Driven Constitutive Relation Reveals Scaling Law for Hydrodynamic Transport Coefficients

摘要： 从密集气体区域到稀薄气体区域都有效的扩展流体力学方程的寻找仍然是一个巨大的挑战。 成功的关键是获得应力和热通量的准确本构关系。 数据驱动模型为从数据中学习本构关系提供了一种新的现象学方法。 这类模型能够通过高阶导数的回归来建立复杂的本构关系，从而扩展牛顿粘性定律和傅里叶热传导定律。 然而，这些模型中导数的选择是随意的，缺乏明确的物理解释。 我们对线性系统上的数据驱动模型进行了理论研究。 我们认为这些模型等价于输运系数的非线性长度尺度标度定律。 与标度定律的等价性验证了数据驱动模型的物理合理性，并揭示了其局限性。 我们的论点还指出，建模标度定律可以避免数据驱动模型中的实际困难，如在噪声数据上的导数估计和变量选择。 我们进一步提出了一种基于标度定律的本构关系模型，并在瑞利散射光谱的计算中进行了测试。 结果表明，我们的数据驱动模型在与 Chapman-Enskog 展开和矩方法相比时具有明显的优势。 显示英文摘要

摘要： 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.