流体动力学中的界面学习：微观-宏观耦合模型中闭包的统计推断
Interface learning in fluid dynamics: statistical inference of closures within micro-macro coupling models
摘要：
流体动力学中的许多复杂多物理场系统涉及在计算域的不同区域中使用具有不同近似水平的求解器来解决流动中存在的多个时空尺度。解决方案的准确性取决于这些求解器之间如何在接口处交换信息，并且已经为这种耦合问题设计了几种方法。在这篇文章中，我们构建了一个数据驱动的模型，通过空间耦合的微观格子玻尔兹曼方法（LBM）求解器和宏观有限差分方法（FDM）求解器的反应扩散系统。微观-宏观求解器之间的耦合在接口处具有一对多的映射，导致接口闭合问题，并且我们提出了基于神经网络的统计推断方法来学习这种闭合关系。在FDM和LBM域之间划分的双保真度设置中，所提出的框架的性能显示了其对复杂系统的承诺，其中微观-宏观求解器之间的分析关系不可用。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
