论文标题
低维模型的操作员推理和物理信息学习不可压缩流
Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows
论文作者
论文摘要
降低的建模在计算流体动力学方面具有悠久的传统。数据对低阶模型的综合的不断增强的意义很好地反映在数据驱动方法的最新成功中，例如动态模式分解和操作员推断。通过这项工作，我们建议一种学习的新方法，用于从数据中使用可压缩流量的结构化低阶模型，该模型可用于工程研究，例如控制，优化和仿真。为此，我们利用Navier-Stokes方程的固有结构来进行不可压缩的流，并表明可以将速度和压力的学习动力学分解，从而导致有效的运算符推理方法来学习不可压缩流的基本动力学。此外，我们使用两个基准问题显示了学习低阶模型中的操作员推断性能，并使用一种侵入性方法，即正交分解以及其他数据驱动的方法进行比较。
Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the recent successes of data-driven approaches such as Dynamic Mode Decomposition and Operator Inference. With this work, we suggest a new approach to learning structured low-order models for incompressible flow from data that can be used for engineering studies such as control, optimization, and simulation. To that end, we utilize the intrinsic structure of the Navier-Stokes equations for incompressible flows and show that learning dynamics of the velocity and pressure can be decoupled, thus leading to an efficient operator inference approach for learning the underlying dynamics of incompressible flows. Furthermore, we show the operator inference performance in learning low-order models using two benchmark problems and compare with an intrusive method, namely proper orthogonal decomposition, and other data-driven approaches.
