Macroscopic descriptions of both natural and engineered materials usually include a number of phenomenological parameters that have to be estimated from experiments or large-scale microscopic simulations. When dealing with advanced complex materials, these descriptions are sometimes not available or not even known. Using sparsity-promoting techniques one can extract macroscopic dynamic models directly from particle-based simulations. In this work, we showcase such an approach on a simple fluid and test its robustness. We introduce a novel measure for automatic macroscopic model selection that combines stability and accuracy of a model. Using this measure and employing only a few physics-based assumptions, we are able to infer both the mass continuity equation and an equation for the conservation of linear momentum. Moreover, the extracted phenomenological and non-phenomenological parameters agree well with their numerically measured values and the well-known semi-empirical estimates. The presented model selection framework can be applied to simulations or experimental data of more complex systems, described in general by a rich set of coupled nonlinear macroscopic equations.

中文翻译：

---

从流体的耗散粒子动力学模拟中学习宏观运动方程


天然材料和工程材料的宏观描述通常包括许多必须通过实验或大规模微观模拟来估计的唯象参数。在处理先进的复杂材料时，这些描述有时不可用或什至不为人所知。使用稀疏性促进技术，我们可以直接从基于粒子的模拟中提取宏观动态模型。在这项工作中，我们在简单流体上展示了这种方法并测试其稳健性。我们引入了一种新的自动宏观模型选择方法，它结合了模型的稳定性和准确性。使用这种方法并仅采用一些基于物理的假设，我们就能够推断出质量连续性方程和线性动量守恒方程。此外，提取的现象学和非现象学参数与其数值测量值和众所周知的半经验估计非常吻合。所提出的模型选择框架可以应用于更复杂系统的模拟或实验数据，通常由一组丰富的耦合非线性宏观方程来描述。