Discovering explicit Reynolds-averaged turbulence closures for turbulent separated flows through deep learning-based symbolic regression with non-linear corrections
arXiv:2301.09048 · doi:10.1063/5.0135638
Abstract
This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier-Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize the paradigm of turbulence modeling. However, due to the black-box essence of most ML methods, it is currently hard to extract interpretable information and knowledge from data-driven models. To address this critical limitation, this work leverages deep learning with symbolic regression methods to discover hidden governing equations of Reynolds stress models. Specifically, the Reynolds stress tensor is decomposed into linear and non-linear parts. While the linear part is taken as the regular linear eddy viscosity model, a long short-term memory neural network is employed to generate symbolic terms on which tractable mathematical expressions for the non-linear counterpart are built. A novel reinforcement learning algorithm is employed to train the neural network to produce best-fitted symbolic expressions. Within the proposed framework, the Reynolds stress closure is explicitly expressed in algebraic forms, thus allowing for direct functional inference. On the other hand, the Galilean and rotational invariance are craftily respected by constructing the training feature space with independent invariants and tensor basis functions. The performance of the present methodology is validated through numerical simulations of three different canonical flows that deviate in geometrical configurations. The results demonstrate promising accuracy improvements over traditional RANS models, showing the generalization ability of the proposed method. Moreover, with the given explicit model equations, it can be easier to interpret the influence of input features on generated models.
References in corpus (28)
- Turbulence Modeling in the Age of Data
- Artificial Neural Networks trained through Deep Reinforcement Learning discover control strategies for active flow control
- A Comprehensive Physics-Informed Machine Learning Framework for Predictive Turbulence Modeling
- Physics-Informed Machine Learning Approach for Augmenting Turbulence Models: A Comprehensive Framework
- RANS Turbulence Model Development using CFD-Driven Machine Learning
- Perspectives on Machine Learning-augmented Reynolds-averaged and Large Eddy Simulation Models of Turbulence
- Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression
- Flow Navigation by Smart Microswimmers via Reinforcement Learning
- Accelerating Deep Reinforcement Learning strategies of Flow Control through a multi-environment approach
- Robust active flow control over a range of Reynolds numbers using an artificial neural network trained through deep reinforcement learning
- RANS Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned
- Scientific multi-agent reinforcement learning for wall-models of turbulent flows
- Physics-guided deep learning framework for predictive modeling of the Reynolds stress anisotropy
- Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks
- A review on Deep Reinforcement Learning for Fluid Mechanics
- A review on deep reinforcement learning for fluid mechanics: an update
- Formulating turbulence closures using sparse regression with embedded form invariance
- Feature selection and processing of turbulence modeling based on an artificial neural network
- Controlling Rayleigh-Bénard convection via Reinforcement Learning
- Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulations
- Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensors
- Learning the aerodynamic design of supercritical airfoils through deep reinforcement learning
- Deep reinforcement learning for large-eddy simulation modeling in wall-bounded turbulence
- Learning nonlocal constitutive models with neural networks
- Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients
- An Iterative Machine-Learning Framework for RANS Turbulence Modeling
- Data augmented turbulence modeling for three-dimensional separation flows
- Contrastive Reinforcement Learning of Symbolic Reasoning Domains