An interpretable framework of data-driven turbulence modeling using deep neural networks

Abstract

Reynolds-averaged Navier–Stokes simulations represent a cost-effective option for practical engineering applications, but are facing ever-growing demands for more accurate turbulence models. Recently, emerging machine learning techniques have had a promising impact on turbulence modeling, but are still in their infancy regarding widespread industrial adoption. Toward their extensive uptake, this paper presents a universally interpretable machine learning (UIML) framework for turbulence modeling, which consists of two parallel machine learning-based modules to directly infer the structural and parametric representations of turbulence physics, respectively. At each phase of model development, data reflecting the evolution dynamics of turbulence and domain knowledge representing prior physical considerations are converted into modeling knowledge. The data- and knowledge-driven UIML is investigated with a deep residual network. The following three aspects are demonstrated in detail: (i) a compact input feature parameterizing a new turbulent timescale is introduced to prevent nonunique mappings between conventional input arguments and output Reynolds stress; (ii) a realizability limiter is developed to overcome the under-constrained state of modeled stress; and (iii) fairness and noise-insensitivity constraints are included in the training procedure. Consequently, an invariant, realizable, unbiased, and robust data-driven turbulence model is achieved. The influences of the training dataset size, activation function, and network hyperparameter on the performance are also investigated. The resulting model exhibits good generalization across two- and three-dimensional flows, and captures the effects of the Reynolds number and aspect ratio. Finally, the underlying rationale behind prediction is explored.

Multi-End Physics-Informed Deep Learning for Seismic Response Estimation

“…Inspired by this, PIDL has been extended to engineering applications. The related studies have involved many communities, including fluid dynamics [ 15 , 23 , 24 ], geology [ 25 ], fatigue analysis [ 26 ], power system [ 27 ], and system identification [ 28 ] and controls [ 29 ]. In PIDL, a conventional strategy is writing the governing PDE into the loss function [ 30 ] to compress the solution space.…”

Predicting the temporal dynamics of turbulent channels through deep learning

“…Recently, machine learning (ML) has offered a third option to enrich the knowledge we have about this subject, also thanks to the development of more powerful deep neural networks (DNNs) over the last years. Some examples include improved modelling results for Reynold-averaged Navier-Stokes (RANS) (Vinuesa et al, 2020) and large-eddy simulations (LESs), flow predictions (Kutz, 2017;Jiménez, 2018;Duraisamy et al, 2019;Brunton et al, 2020;Jiang et al, 2021;Guastoni et al, 2021), flow control and optimization strategies (Rabault et al, 2019;Raibaudo et al, 2020;Vinuesa et al, 2022), generation of inflow conditions (Fukami et al, 2019b), extraction of flow patterns (Raissi et al, 2020;Eivazi et al, 2021a,b), machine-learning-based reduced-order models (Nakamura et al, 2021;Vinuesa and Brunton, 2021) and prediction of the temporal dynamics (Srinivasan et al, 2019;Eivazi et al, 2020). The capability of a network to predict the temporal evolution of a turbulent flow is the focus of this study.…”

Machine-Learning Methods for Complex Flows

“…Flow control is another topic where deep learning exhibits potential, in particular, through deep reinforcement learning [24,25]. Turbulence modelling, e.g., through Reynolds-averaged Navier-Stokes (RANS) methods, has also experienced an important development via ML through interpretable models [26][27][28]. Furthermore, flow optimization [29] and the development of inflow conditions [30] have also been facilitated via recent developments in data-driven methods.…”