Data-Driven Methods for Turbulent Flow and Noise Prediction
Data-Driven Methods for Turbulent Flow and Noise Prediction
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PINN-LEE:
PINN-LEE:
Physics-Informed Neural Networks - Linearized Euler Equations
Physics-Informed Neural Networks - Linearized Euler Equations
In our research group, we not only utilize traditional computational techniques but are also eager to explore the limits of scientific machine learning methods and their applications in aerodynamics and aeroacoustics, aiming to develop frameworks that effectively leverage existing data.
In this context, we introduced PINN-LEE, a Physics-Informed Neural Networks (PINNs)-based aeroacoustic solver. PINNs enable the creation of a mapping between the input and output states of a physical system by incorporating the governing equation residual as a physical loss term. This physical loss allows us to learn these mappings even in cases where known data is limited or completely missing, except for boundary and initial conditions—which are typically also required in traditional partial differential equation (PDE) solvers.
Although PINNs are a highly popular technique across various engineering applications, their use in aeroacoustics remains very limited. Our research aims to employ this method to replace the Linearized Euler Equations (LEE) step in an aeroacoustic prediction framework with a data-driven counterpart. More specifically, PINN-LEE is applied as the third step in the framework, following the CFD solution and aeroacoustic source calculation. One benefit of using a data-driven noise propagation approach after CFD is that the necessary training data can be generated during the CFD simulation itself, which is already typically required for aerodynamic performance evaluation.
PINNs are a promising alternative to address limitations of traditional LEE solvers, which often suffer from numerical dissipation, instabilities, and the need to generate a new computational grid different from that of the CFD simulation. PINNs offer a mesh-free environment with smooth analytical functions whose derivatives are not directly affected by numerical instabilities. Additionally, for far-field noise prediction, the need to implement an artificial absorbing boundary condition is eliminated thanks to the continuous nature of neural networks. However, this also introduces challenges for training PINN-LEE, as the known data come from a concentrated region, turning the problem into a direct extrapolation task with the absence of initial and boundary conditions.
Our recent research focuses on overcoming these challenges and enhancing the capabilities of the PINN-LEE framework, while also contributing to the scientific machine learning literature.
The ultimate goal of this research is to develop a framework that enables simultaneous training of the PINN-LEE model alongside the CFD solver. Such a framework has the potential to eliminate the extra time needed to perform noise propagation with a separate setup and to provide highly accurate far-field noise predictions shortly after the CFD stage is completed.
Related Publications
Ugur, L., Karpe, S.B., Huang, P., Zhou, B. (2025), “PINN-LEE: Physics-Informed Neural Networks Framework to Solve Linearized Euler Equations for Aeroacoustic Predictions”, AIAA Aviation Forum, 21-25 July 2025, Las Vegas, NV (To appear).
Physics-Informed Field Inversion Machine Learning-based Stochastic Noise Generation (PIFIML-SNG)
Physics-Informed Field Inversion Machine Learning-based Stochastic Noise Generation (PIFIML-SNG)
Accurate synthetic turbulence generation has long been a desired, yet challenging capability in aerodynamics and aeroacoustic applications. It can be used to trigger realistic turbulent flow fields, such as the transition from RANS to LES in hybrid models, or to model unsteady sources in a flow field.
One approach used to replace computationally intensive, time-dependent CFD solutions is Stochastic Noise Generation (SNG), which was originally developed to estimate source terms for aeroacoustic predictions efficiently. The method generates a turbulent velocity field based on a given RANS solution. Its energy-spectrum-based analytical modeling enables the prediction of realistic synthetic turbulent velocity fields within seconds.
In our studies, we not only enhanced the predictive capability of SNG through equation-level modifications but also corrected its empirical parameters using spatial and modal corrections via the Field Inversion Machine Learning (FIML) technique. This approach allows us to adjust the model behavior by assimilating available data with a high degree of flexibility. The assimilated data are then used to train machine learning models that provide optimal model parameters for unseen cases in less than a second. This framework enables the prediction of useful turbulent velocity fields in seconds—compared to the hours required for high-fidelity simulations.
The modal correction stage is particularly unique in FIML applications, allowing optimal correction prediction from a steady solution. This enhancement enables correction of time-dependent flow properties in addition to spatial ones, resulting in more accurate turbulence generation suitable for broadband noise propagation.
Additionally, to generate convection-aware flow fields, we proposed a physics-informed data assimilation stage as part of this study. This novel approach not only improves the inversion process but also enables field inversion with sparse measurements.
Related Publications
Ugur, L. and Zhou, B. (2025), “Data-Driven Stochastic Turbulence Generation via Physics-Informed Field Inversion Machine Learning”, 1st International AI and Fluid Mechanics Symposium, 27-30 May 2025, Chania, Greece (To appear).
Ugur, L., Kunz, F., Zhou, B. (2024), “Field Inversion Machine Learning-based Stochastic Noise Generation Model for Jet Noise Predictions”, 30th AIAA/CEAS Aeroacoustics Conference, 4-7 June 2024, Rome. https://doi.org/10.2514/6.2024-3127 (Best Student Paper Award)
Multi-Fidelity Data-Driven Noise Prediction
Multi-Fidelity Data-Driven Noise Prediction
A key challenge in turbulence and noise modelling is to improve the predictive accuracy of low/mid fidelity numerical models without resorting to excessive reliance on high-fidelity (HiFi) data. In collaboration with Prof. Xun Huan’s group at the University of Michigan and Dr. Nick Zang at the Queen Mary University of London, we have developed a multi-fidelity machine learning (MFML) framework, based on transfer learning (TL) and active learning (AL). In particular, TL is used to incorporate information from multiple fidelity of data sources consisting of a large data set from inexpensive low-fidelity (LoFi) simulations and a limited amount of HiFi data. The machine learning (ML) model is further improved, iteratively, by performing additional HiFi simulations/experiments selected based on an AL algorithm designed to progressively minimize the predictive error of the ML model. This allows for the HiFi data to be infused and tightly integrated into a prediction and optimization framework. This methodology was demonstrated on the noise prediction of propellers, where the LoFi propeller noise model is iteratively enhanced using the TL and AL techniques, with a small HiFi dataset obtained from wind-tunnel experiments. Once trained, this MFML model enables rapid prediction of propeller noise given its geometry and operating conditions, at significantly higher accuracy than those trained with only LoFi or HiFi data.
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