New generation of machine-learning based Models for Aerodynamics Computations – NEWMAC

This project aims at investigating ML/AI solutions to correct and improve the turbulent models in the RANS formulation. To attend to this task, one of the most established method today is the so-called field-inversion / machine-learning approach (FI/ML) by Parish & Duraisamy (2016). The classical FI/ML method is based on two steps. The first step is the field-inversion step. This step determines a RANS turbulence model correction term by field inversion. This is done numerically by employing an adjoint flow solver. For this purpose, a numerical optimization problem is solved, minimising the deviation of the corrected RANS model from target reference data. In the present work, reference data are understood to be highly reliable data from experiments or from Direct Numerical Simulation or Large-Eddy Simulation. The correction term is a field function of spatial coordinates. This minimization problem might be strongly underdetermined and is ill-posed especially when the reference data stems from experiments in 3D configurations where only few measurements are available. The second step is the machine-learning step and infers a turbulence model augmentation term whose arguments are physical flow features (also called input flow features). This is accomplished using ML techniques. The ML step yields a ML-based (or: AI-based) RANS correction module, which can be plugged into a RANS solver.

Data assimilation has been a core research topic at ONERA for the past years. Regarding the NEWMAC project, we assimilated transonic flows around an airfoil using only surface pressure data. We tested multiple parameters and successfully corrected the one-equation Spalart-Allmaras RANS model. On top of that, despite using only surface data during the optimization, the Mach number field was equally corrected, marking a significant milestone for our approach. This work performed during an internship will be pursued in a PhD program within the NEWMAC consortium.
More refined models, such as the Differential Reynolds Stress Model (DRSM), solve transport equations for each component of the Reynolds stress tensor, providing a more detailed representation of turbulent flows compared to simpler models by accounting for anisotropy and complex flow features. Despite the excellent results achieved through the use of data-assimilation techniques on the SA one-equation model, there is still nothing in the literature about their application to RSM. Thus, a doctoral thesis is in progress to correct this type of more advanced turbulence models focusing corner flows and separated flows, in which classical RANS simulations fail to reproduce key flows characteristics. By the end of the thesis, we should have a new data-driven DRSM model built using data-assimilation and machine-learning techniques.
The filed-inversion/machine learning discussed so far is a two-step procedure. However, it is possible to combine the two-step procedure into a single method. This means that the optimization of the field-inversion step will be achieved by optimizing the ML structure itself. This will be achieved with an end-to-end system that leverages Convolutional Neural Networks (CNNs) or Graph Neural Networks (GNNs) coupled with Deep Equilibrium Models (DEQs). The proposed method utilizes the BROADCAST solver, developed at ONERA, which incorporates Tapenade for Automatic Differentiation (AD). This feature allows the calculation of the adjoint operator, facilitating the correction of backpropagation in the DEQ layer.
In regard to the ML part, in a recent publication, we trained, validated and compared two types of ML-based models to augment Reynolds-averaged Navier-Stokes (RANS) simulations. The methodology was tested in flows around bumps. The ML-based models were trained in four configurations presenting attached flow, small and moderate separations and tested in a configuration presenting large separation. The output quantity of the machine-learning model is the normalized turbulent viscosity. The new models based on artificial neural networks (NN) and random forest (RF) improved the results if compared to the baseline Spalart-Allmaras model, in terms of velocity field and skin-friction profiles.

The subject addressed in this project is not simple and requires advanced methodologies and innovative approaches through the use of machine learning. The Principal Investigator (PI) is confident that the progress made so far aligns well with the initial planning and objectives of the project. Significant milestones have been achieved, and the groundwork has been laid for impactful outcomes. In the coming months, we anticipate making critical advancements, particularly in refining and enhancing numerical RANS models. These improvements are expected to bridge the gap between theoretical research and practical industrial applications. This progression not only underscores the project's relevance but also highlights its potential to drive innovation in industrial numerical modeling.

1. Volpiani, P. S. (2024). Are random forests better suited than neural networks to augment RANS turbulence models?. International Journal of Heat and Fluid Flow, 107, 109348.
2. Volpiani, P. S. (2024). Improving RANS turbulence models using random forests and neural networks. In International Conference on Computational Fluid Dynamics-ICCDF12.

In this project, we study new machine-learning methodologies to improve statistical turbulence models for aeronautical applications. In aerodynamics, currently used turbulence models in industry are based on strong approximations and are tuned on very simple configurations. Such models exhibit strong weaknesses as soon as more complex industrial flows are considered. Machine-learning techniques may leverage the wealth of numerical high-fidelity and (incomplete) experimental data that is currently available to improve such models. ONERA / DLR / SAFRAN TECH / ROLLS-ROYCE intend to explore and improve the so-called field-inversion (FI)-machine learning (ML) methodology introduced recently by Duraisamy. The goal is to explore more sophisticated turbulence models, new AI-based techniques for the regularisation of the FI step in the case of incomplete reference data, new systematic tools for the selection of input flow features, and new learning strategies. These disruptive methodologies will be incorporated within numerical platforms that allow CFD codes to take advantage of data-driven techniques. The capabilities of such tools will finally be evaluated and assessed on industrially relevant configurations, such as an aircraft in high-lift configuration and a compressor cascade.