Machine Learning enhanced parametric Reynolds-averaged Navier-Stokes equations at the full and reduced order levels

2025/10/08 by Davide Oberto, Oberto, Davide, Maria Strazzullo +3
Engineering · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #G.1.8 #Lattice Boltzmann Simulation Studies #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2510.06992

openalex publication_date 2025/10/08 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

In this contribution, we focus on the Reynolds-Averaged Navier-Stokes (RANS) models and their exploitation to build reliable reduced order models to further accelerate predictions for real-time applications and many-query scenarios. Specifically, we investigate how machine learning can be employed to enhance the predictive capabilities of the model, both at the Full Order Model (FOM) and Reduced Order Model (ROM) levels. We explore a novel integration of these two areas. We generate the FOM snapshots, essential for ROM construction, using a data-driven RANS model: the ν_t-Vector Basis Neural Network. This is the first time that these machine learning procedure generalizes a large parametric variation, and we propose tailored training strategies to increase the accuracy of the FOM model. At the ROM level, we compare the results obtained by standard Proper Orthogonal Decomposition in an intrusive Galerkin setting (PODG) and POD Neural Network approach (PODNN). The numerical validation is based on a classic turbulent flow benchmark: the flow in a square duct. Our investigation reveals that the PODG method, proves unstable and inaccurate for turbulent flow prediction, while PODNN demonstrates superior performance in terms of accuracy and computational efficiency.

Citations

• Data-driven Optimization for the Evolve-Filter-Relax regularization of convection-dominated flows
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• Hybrid Data-Driven Closure Strategies for Reduced Order Modeling
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• Data-Driven POD-Galerkin Reduced Order Model for Turbulent Flows
• Efficient Geometrical parametrization for Finite-Volume based Reduced Order Methods
• Theory of Representations for Tensor Functions—A Unified Invariant Approach to Constitutive Equations
• Tackling Turbulence with Supercomputers

Related

• Parametric Intrusive Reduced Order Models enhanced with Machine Learning Correction Terms
• Incorporating basic calibrations in existing machine-learned turbulence modeling
• Hybrid Reduced-Order Models for Turbulent Flows Using Recurrent Neural Architectures
• A Closed Machine Learning Parametric Reduced Order Model Approach -- Application to Turbulent Flows
• Improving the Vector Basis Neural Network for RANS Equations Using Separate Trainings