Session E31: Computational Fluid Dynamics: Data-Driven Modeling

On the Conditioning of Machine-Learning-Assisted Turbulence Modeling

Recently, several researchers have demonstrated that machine learning techniques can be used to improve the RANS modeled Reynolds stress by training on available database of high fidelity simulations. However, obtaining improved mean velocity field remains an unsolved challenge, restricting the predictive capability of current machine-learning-assisted turbulence modeling approaches. In this work we define a condition number to evaluate the model conditioning of data-driven turbulence modeling approaches, and propose a stability-oriented machine learning framework to model Reynolds stress. Two canonical flows, the flow in a square duct and the flow over periodic hills, are investigated to demonstrate the predictive capability of the proposed framework. The satisfactory prediction performance of mean velocity field for both flows demonstrates the predictive capability of the proposed framework for machine-learning-assisted turbulence modeling. With showing the capability of improving the prediction of mean flow field, the proposed stability-oriented machine learning framework bridges the gap between the existing machine-learning-assisted turbulence modeling approaches and the demand of predictive capability of turbulence models in real applications.   

Data-Driven Augmentations of Second Moment Closures for Turbulent Flow Prediction

Second moment closures of turbulence - while having the potential to faithfully represent key turbulence processes - have not yet proven to offer significantly improved accuracy compared to linear eddy viscosity closures in practical problems. While meticulous theories are used to define models for pressure strain and near-wall dissipation anisotropy, the net imbalance in errors in the structural form of the modeled terms has traditionally limited the accuracy of these models. In this work, we address these model-form uncertainties using a framework based on inverse modeling and machine learning. We embed discrepancy functions within the governing equations of the simulation model. In contrast to parametric models, we seek the functional form of the model discrepancy. Once the spatio-temporal forms of the discrepancy function is inferred, machine learning is used to reconstruct the discrepancy functions in terms of local, Galilean invariant variables. The final step is to embed the learned discrepancy terms into the model equations. When uncertainties in the data and the inversion step are propagated to the embedded discrepancy term, bounds can be obtained in the predictive results by sampling the discrepancy terms. Results are demonstrated on wall-bounded turbulent flows.   

A neural network approach for the blind deconvolution of turbulent flows

We present a single-layer feedforward artificial neural network architecture trained through a supervised learning approach for the deconvolution of flow variables from their coarse grained computations such as those encountered in large eddy simulations. We stress that the deconvolution procedure proposed in this investigation is blind, i.e. the deconvolved field is computed without any pre-existing information about the filtering procedure or kernel. This may be conceptually contrasted to the celebrated approximate deconvolution approaches where a filter shape is predefined for an iterative deconvolution process. We demonstrate that the proposed blind deconvolution network performs exceptionally well in the a-priori testing of both two-dimensional Kraichnan and three-dimensional Kolmogorov turbulence and shows promise in forming the backbone of a physics-augmented data-driven closure for the Navier-Stokes equations.   

Deep Learning Fluid Mechanics

We have developed a new data-driven model paradigm for the rapid inference and solution of the constitutive equations of fluid mechanic by deep learning models. Using generative adversarial networks (GAN), we train models for the direct generation of solutions to steady state heat conduction and incompressible fluid flow without knowledge of the underlying governing equations. Rather than using artificial neural networks to approximate the solution of the constitutive equations, GANs can directly generate the solutions to these equations conditional upon an arbitrary set of boundary conditions. Both models predict temperature, velocity and pressure fields with great test accuracy (\textgreater 99.5{\%}). The application of our framework for inferring and generating the solutions of partial differential equations can be applied to any physical phenomena and can be used to learn directly from experiments where the underlying physical model is complex or unknown. We also have shown that our framework can be used to couple multiple physics simultaneously, making it amenable to tackle multi-physics problems.   

A Deep Learning based Approach to Reduced Order Modeling of Fluids using LSTM Neural Networks

Reduced Order Modeling (ROM) can be used as surrogates to prohibitively expensive simulations to model flow behavior for long time periods. ROM is predicated on extracting dominant spatio-temporal features of the flow from CFD or experimental datasets. We explore ROM development with a deep learning approach, which comprises of learning functional relationships between different variables in large datasets for predictive modeling. Although deep learning and related artificial intelligence based predictive modeling techniques have shown varied success in other fields, such approaches are in their initial stages of application to fluid dynamics. Here, we explore the application of the Long Short Term Memory (LSTM) neural network to sequential data, specifically to predict the time coefficients of Proper Orthogonal Decomposition (POD) modes of the flow for future timesteps, by training it on data at previous timesteps. The approach is demonstrated by constructing ROMs of several canonical flows. Additionally, we show that statistical estimates of stationarity in the training data can indicate a priori how amenable a given flow-field is to this approach. Finally, the potential and limitations of deep learning based ROM approaches will be elucidated and further developments discussed.   

Deep learning of unsteady laminar flow over a cylinder

Unsteady flow over a circular cylinder is reconstructed using deep learning with a particular emphasis on elucidating the potential of learning the solution of the Navier-Stokes equations. A deep neural network (DNN) is employed for deep learning, while numerical simulations are conducted to produce training database. Instantaneous and mean flow fields which are reconstructed by deep learning are compared with the simulation results. Fourier transform of flow variables has been conducted to validate the ability of DNN to capture both amplitudes and frequencies of flow motions. Basis decomposition of learned flow is performed to understand the underlying mechanisms of learning flow through DNN. The present study suggests that a deep learning technique can be utilized for reconstruction and, potentially, for prediction of fluid flow instead of solving the Navier-Stokes equations.