Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

By Julia Ling, A. Kurzawski, Jeremy A. Templeton. 2016

1,578 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Steven L. Brunton
2. Heng Xiao
3. Ricardo Vinuesa
4. Paola Cinnella
5. Karthik Duraisamy
6. Nils Thürey
7. Jin-Long Wu
8. G. Em Karniadakis

In Statistical and Nonlinear Physics

1. Steven L. Brunton
2. G. Em Karniadakis
3. Ricardo Vinuesa
4. Heng Xiao
5. Nicholas Zabaras
6. Paola Cinnella
7. Michael S. Steinbach
8. Karthik Duraisamy

Citations in the corpus

• Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow (2018, methodology): “Other works create velocity field predictions by learning parameters for Reynolds Averaged Navier Stokes models from simulation data [LKT16].”
• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data (2019, neutral): “Reynolds-Averaged Navier-Stokes simulations [12, 13, 14] and others.”
• Mean Field Analysis of Neural Networks: A Law of Large Numbers (2018, methodology): “Neural networks are being used in reduced-form models of the Navier--Stokes equation in turbulent conditions (see [34] and [35]).”
• DGM: A deep learning algorithm for solving partial differential equations (2017, positive): “[32] uses a deep neural network to model the Reynolds stresses in a Reynolds-averaged Navier-Stokes (RANS) model.”
• Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework (2017, methodology): “using random forests [16] and deep neural networks [17].”
• Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoils (2016, methodology): “[30] used neural networks to reconstruct aij and propagate the model to velocity field predictions.”
• Using Machine Learning to Parameterize Moist Convection: Potential for Modeling of Climate, Climate Change, and Extreme Events (2018, methodology): “The use of ML is also currently being explored for subgrid turbulence modeling for engineering applications [e.g., Ling et al. , 2016; Wang et al. , 2017].”
• Enforcing Analytic Constraints in Neural Networks Emulating Physical Systems. (2019, background): “Despite the need for physically informed NNs for complex physical systems [2–5], enforcing hard constraints [6] has been limited to physical systems governed by specific equations, such as advection equations [7–9], Reynolds-averaged Navier-Stokes equations [10,11], boundary conditions of idealized ”
• Turbulence Modeling in the Age of Data (2018, background): “The work of Ling and Templeton (2015) illustrated a scheme for crafting features based on flow physics and normalizing them using local quantities; later work has expanded this approach by using invariants of a tensorial set (Ling et al. 2016a).”
• Informed Machine Learning – A Taxonomy and Survey of Integrating Prior Knowledge into Learning Systems (2019, methodology): “sors [50], or the physical Minkowski metric that reflects mass invariance can be integrated via a Lorentz layer into a neural network [51].”