BOOST: Boosting Linearized Mean-Field Methods using Physics Informed Neural Networks

基于线性化Navier-Stokes方程的流体力学分析和预测已被证明是流体力学的有效工具。它们允许在非定常流动中识别驱动机制，并提供对潜在物理的见解。因此，这些线性化方法被应用于许多领域，例如流体力学、气动声学、燃烧动力学以及一般的流动控制。然而，由于方程是围绕基本状态线性化的，因此需要将基本状态作为方法的输入。最初，控制方程是围绕基流（流的稳定状态）线性化的，以预测不稳定的开始。然而，最近的研究表明，分析也可以基于平均（时间平均）场，这为湍流的分析开辟了道路。平均场通常可以从非定常CFD模拟或实验中提取，这给计算带来了一些挑战。一个经常遇到的问题是，线性化方程往往是基于一个简化的方程集，这与平均场不一致。因此，在线性化方程中正确选择湍流模型是一个关键问题。此外，从实验中提取的数据通常是稀疏的，这意味着物理量有限，空间分辨率有限或仅限于域的某些区域。BOOST项目的中心目标是利用机器学习的最新进展，并开发一致且鲁棒的线性化平均场框架。其核心思想是使用物理信息神经网络（PINN）进行平均场数据同化。PINN是一种映射，允许在物理约束下近似函数。同化允许识别隐藏变量，例如涡流粘度场。这为线性化方程提供了一致的闭包，并开启了将线性化平均场方法应用于需要多个闭包的更复杂问题的阶段，例如湍流反应流。通过这种方式，创建了一个整体框架，允许通过相同的线性化求解器处理各种问题。此外，pin码用于基于物理的外推。基于已知的域内某一区域的平均场，可以重构出无法进行PIV测量的隐藏区域的平均场。这将改善流动动力学的分析和预测，因为许多流体动力学不稳定性的起源远高于观测场。BOOST中将要开发的工具构成了线性化平均场方法的一个飞跃。应用范围包括改进的流体动力学预测，更好地理解底层物理，改进的起源分析和主导结构的可接受性，所有这些都是通过使用易于使用的机器学习算法采用平均场来实现的。

The analysis and prediction of fluid dynamics based on the linearized Navier-Stokes equations have proven to be effective tools in fluid mechanics. They allow the identification of driving mechanisms in unsteady flows and give insights into the underlying physics. Therefore, these linearized methods are applied in many fields, e.g., in hydrodynamics, aeroacoustics, combustion dynamics and generally for flow control. However, as the equations are linearized around a base state, the base state is required as an input to the methods. Originally, the governing equations were linearized around the base flow (the stable state of the flow) to predict the onset of an instability. However, recent studies show that the analysis may also be based on the mean (time-averaged) field, which opens the way for the analysis of turbulent flows. Mean-fields can generally be extracted from unsteady CFD simulations or experiments, which poses several challenges. One often encountered problem is that the linearized equations are often based on a reduced set of equations, which is inconsistent with the mean-fields. A key question is thereby the right choice of turbulence model in the linearized equations. Moreover, data extracted from experiments is often sparse, meaning limited in physical quantities, limited in spatial resolution or limited to certain areas of the domain. The central goal of the BOOST project is to use recent advances in Machine Learning and to develop a consistent and robust linearized mean-field framework. The core idea is to use Physics Informed Neural Networks (PINN) for mean-field data assimilation. PINN is a mapping that allows to approximate functions under physical constraints. The assimilation allows to identify hidden variables, such as for example an eddy viscosity field. This provides a consistent closure for the linearized equations and opens the stage to apply linearized mean-field methods to more complex problems that require multiple closures, such as for example turbulent reacting flows. In this way, a holistic framework is created that allows a variety of problems to be handled by the same linearized solver. Furthermore, PINNs are used for physics-based extrapolation. Based on a known mean-field in a certain area of the domain, the mean-field in a hidden area, where for example PIV measurements are unfeasible, can be reconstructed. This will improve the analysis and prediction of flow dynamics, as many hydrodynamic instabilities have their origin far upstream of the observed field. The tools that are to be developed in BOOST constitute a leap forward for linearized mean-field methods. The application range encompasses improved prediction of flow dynamics, better understanding of the underlying physics, improved analysis of the origin and receptivity of dominant structures, all realized by an adoption of the mean-fields by means of an easy-to-use Machine Learning algorithm.