Machine Learning Methods for Data-Driven Turbulence Modeling

Zhang, Ze Jia; Duraisamy, Karthik

doi:10.2514/6.2015-2460

Cited by 110 publications

(80 citation statements)

References 14 publications

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“…Recently, these approaches have been extended to the field of engineering mechanics, such as learning constitutive models in solid mechanics [12][13][14], surrogate models in fluid mechanics [15][16][17] and physical models or governing equations purely extracted from the collected data [18][19][20]. In conjunction with machine learning techniques such as manifold learning [21] or neural networks [22], the recent studies [23][24][25] offer a new paradigm for data-driven computing for various applications such as design of materials [26].…”

Section: Introductionmentioning

confidence: 99%

A physics-constrained data-driven approach based on locally convex reconstruction for noisy database

Chen

2020

Computer Methods in Applied Mechanics and Engineering

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Physics-constrained data-driven computing is a hybrid approach that integrates universal physical laws with data-based models of experimental data to enhance the scientific computing. A new data-driven simulation approach enriched with a locally convex reconstruction, termed the local convexity data-driven (LCDD) computing, is proposed to enhance accuracy and robustness against noise and outliers in data sets in the data-driven computing. In this approach, for a given state obtained by the physical simulation, the corresponding optimum experimental solution is sought by projecting the state onto the associated local convex manifold reconstructed based on the nearest experimental data. This learning process of local data structure is less sensitivity to noisy data and consequently yields better accuracy. A penalty relaxation is also introduced to recast the local learning solver in the context of non-negative least squares that can be solved effectively. The reproducing kernel approximation with stabilized nodal integration are employed for the solution of the physical manifold to allow reduced stress-strain data at the discrete points for enhanced effectiveness in the LCDD learning solver. Due to the inherent manifold learning properties, LCDD performs well for high-dimensional data sets that are relatively sparse in real-world engineering applications. Numerical tests demonstrated that LCDD enhances nearly one order of accuracy compared to the standard distance-minimization data-driven scheme when dealing with noisy database, and a linear exactness is achieved when local stress-strain relation is linear.

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Section: Introductionmentioning

confidence: 99%

A physics-constrained data-driven approach based on locally convex reconstruction for noisy database

Chen

2020

Computer Methods in Applied Mechanics and Engineering

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“…Details of the machine learning aspect of our work are discussed in a companion paper. 15 The machine learned algorithm is then injected back into the computational solver, where it is queried in a predictive fashion. The output of the machine learned algorithm is then filtered through the final Bayesian inference step, which combines the information gained through the entire inverse/machine learning process with the prior, to produce a final posterior prediction of the corrective source term.…”

Section: Model Predictionmentioning

confidence: 99%

“…Although the resulting model is only valid/accurate for the problem used to generate it, attempts to generalize it using machine learning are a part of our ongoing work. 11,15 A Bayesian approach 16 is used to solve the inverse problem. β is considered to be a random function with a certain probability distribution.…”

Section: Inversionmentioning

confidence: 99%

Quantification of Turbulence Modeling Uncertainties Using Full Field Inversion

Parish

Duraisamy

2015

22nd AIAA Computational Fluid Dynamics Conference

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Reynolds Averaged Navier-Stokes (RANS) turbulence models have historically been developed using a combination of theoretical/physical/mathematical arguments, modeler expertise, and empirical data-fitting. As a consequence of the loss of information incurred during the ensemble averaging process, RANS model development has always been data-driven, to an extent, out of necessity. With the profusion of high resolution simulations and experimental methods, there exists a prodigious opportunity to more comprehensively inform closure models with data and improve their utlility in practical predictions of complex turbulent flows. In contrast to inferring model parameters, this work uses inverse modeling to directly obtain corrective, spatially distributed terms that are consistent with the predictive RANS models, thus offering a route to address the issue of model discrepancy which has long plagued turbulence model development. The posterior distributions of the inferred terms are quantified using Bayesian inversion and sampling. Results are presented for turbulent channel flow and flows with wall curvature. While the source terms inferred in this work are problem dependent, an ongoing subset of our work is to use machine learning methodologies to obtain general functional forms of the type that are inferred in this work. This paper specifically focuses on the mechanics of Bayesian inversion and its implications on the quantification of errors and uncertainties in turbulence modeling.

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“…In fluid mechanics, ANN have been applied to the study of turbulent flows, as a data-mining tool to build predictive models associated with direct numerical simulations. Specifically, these predictive models have been used to obtain correction factors in turbulent production terms 14 or to estimate flow uncertainties 15 . ANN have also been employed to improve and facilitate turbulence modeling [16][17][18] .…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic object identification with artificial neural models

Lakkam

Balamurali

Bouffanais

2019

Sci Rep

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The lateral-line system that has evolved in many aquatic animals enables them to navigate murky fluid environments, locate and discriminate obstacles. Here, we present a data-driven model that uses artificial neural networks to process flow data originating from a stationary sensor array located away from an obstacle placed in a potential flow. The ability of neural networks to estimate complex underlying relationships between parameters, in the absence of any explicit mathematical description, is first assessed with two basic potential flow problems: single source/sink identification and doublet detection. Subsequently, we address the inverse problem of identifying an obstacle shape from distant measures of the pressure or velocity field. Using the analytical solution to the forward problem, very large training data sets are generated, allowing us to obtain the synaptic weights by means of a gradient-descent based optimization. The resulting neural network exhibits remarkable effectiveness in predicting unknown obstacle shapes, especially at relatively large distances for which classical linear regression models are completely ineffectual. These results have far-reaching implications for the design and development of artificial passive hydrodynamic sensing technology.

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Machine Learning Methods for Data-Driven Turbulence Modeling

Cited by 110 publications

References 14 publications

A physics-constrained data-driven approach based on locally convex reconstruction for noisy database

A physics-constrained data-driven approach based on locally convex reconstruction for noisy database

Quantification of Turbulence Modeling Uncertainties Using Full Field Inversion

Hydrodynamic object identification with artificial neural models

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