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

• Applicant: Professor Dr.-Ing. Kilian Oberleithner
• Subject Area: Fluid Mechanics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 506170981

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.

• DFG Programme: Research Grants