论文标题
流体动力学中的界面学习：微麦克罗耦合模型中关闭的统计推断
Interface learning in fluid dynamics: statistical inference of closures within micro-macro coupling models
论文作者
论文摘要
流体动力学中的许多复杂多物理系统涉及使用具有不同近似值的求解器，以解决计算域的不同区域，以解决流动中存在的多个时空尺度。解决方案的准确性受界面上这些求解器之间交换的信息以及为这种耦合问题设计的几种方法的控制。在本文中，我们通过将微观晶格Boltzmann方法（LBM）求解器和Macroscale有限差方法（FDM）求解器用于反应扩散系统来构建数据驱动模型。微麦克罗求解器之间的耦合在导致接口封闭问题的界面上具有一对映射，我们提出了一种基于神经网络的统计推理方法，以学习这种封闭关系。在FDM和LBM域之间分配的双歧度设置中所提出的框架的性能显示了其对微观摩克罗求解器之间分析关系的复杂系统的希望。
Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of the solution is governed by how the information is exchanged between these solvers at the interface and several methods have been devised for such coupling problems. In this article, we construct a data-driven model by spatially coupling a microscale lattice Boltzmann method (LBM) solver and macroscale finite difference method (FDM) solver for reaction-diffusion systems. The coupling between the micro-macro solvers has one to many mapping at the interface leading to the interface closure problem, and we propose a statistical inference method based on neural networks to learn this closure relation. The performance of the proposed framework in a bifidelity setting partitioned between the FDM and LBM domain shows its promise for complex systems where analytical relations between micro-macro solvers are not available.
