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Register a new userProbabilistic neural network-based reduced-order surrogate for fluid flows
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In recent years, there have been a surge in applications of neural networks (NNs) in physical sciences. Although various algorithmic advances have been proposed, there are, thus far, limited number of studies that assess the interpretability of neural networks. This has contributed to the hasty characterization of most NN methods as black boxes and hindering wider acceptance of more powerful machine learning algorithms for physics. In an effort to address such issues in fluid flow modeling, we use a probabilistic neural network (PNN) that provide confidence intervals for its predictions in a computationally effective manner. The model is first assessed considering the estimation of proper orthogonal decomposition (POD) coefficients from local sensor measurements of solution of the shallow water equation. We find that the present model outperforms a well-known linear method with regard to estimation. This model is then applied to the estimation of the temporal evolution of POD coefficients with considering the wake of a NACA0012 airfoil with a Gurney flap and the NOAA sea surface temperature. The present model can accurately estimate the POD coefficients over time in addition to providing confidence intervals thereby quantifying the uncertainty in the output given a particular training data set.
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We investigate the applicability of machine learning based reduced order model (ML-ROM) to three-dimensional complex flows. As an example, we consider a turbulent channel flow at the friction Reynolds number of $Re_tau=110$ in a minimum domain which can maintain coherent structures of turbulence. Training data set are prepared by direct numerical simulation (DNS). The present ML-ROM is constructed by combining a three-dimensional convolutional neural network autoencoder (CNN-AE) and a long short-term memory (LSTM). The CNN-AE works to map high-dimensional flow fields into a low-dimensional latent space. The LSTM is then utilized to predict a temporal evolution of the latent vectors obtained by the CNN-AE. The combination of CNN-AE and LSTM can represent the spatio-temporal high-dimensional dynamics of flow fields by only integrating the temporal evolution of the low-dimensional latent dynamics. The turbulent flow fields reproduced by the present ML-ROM show statistical agreement with the reference DNS data in time-ensemble sense, which can also be found through an orbit-based analysis. Influences of the population of vortical structures contained in the domain and the time interval used for temporal prediction on the ML- ROM performance are also investigated. The potential and limitation of the present ML-ROM for turbulence analysis are discussed at the end of our presentation.
We investigate the capability of neural network-based model order reduction, i.e., autoencoder (AE), for fluid flows. As an example model, an AE which comprises of a convolutional neural network and multi-layer perceptrons is considered in this study. The AE model is assessed with four canonical fluid flows, namely: (1) two-dimensional cylinder wake, (2) its transient process, (3) NOAA sea surface temperature, and (4) $y-z$ sectional field of turbulent channel flow, in terms of a number of latent modes, a choice of nonlinear activation functions, and a number of weights contained in the AE model. We find that the AE models are sensitive against the choice of the aforementioned parameters depending on the target flows. Finally, we foresee the extensional applications and perspectives of machine learning based order reduction for numerical and experimental studies in fluid dynamics community.
We consider the use of probabilistic neural networks for fluid flow {surrogate modeling} and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the inputs. Consequently, the overall formulation sets up a procedure to predict the hyperparameters of this distribution which are then used to compute an objective function given training data. We demonstrate that this framework has the ability to provide for prediction confidence intervals based on the assumption of a probabilistic posterior, given an appropriate model architecture and adequate training data. The applicability of the present framework to cases with noisy measurements and limited observations is also assessed. To demonstrate the capabilities of this framework, we consider canonical regression problems of fluid dynamics from the viewpoint of reduced-order modeling and spatial data recovery for four canonical data sets. The examples considered in this study arise from (1) the shallow water equations, (2) a two-dimensional cylinder flow, (3) the wake of NACA0012 airfoil with a Gurney flap, and (4) the NOAA sea surface temperature data set. The present results indicate that the probabilistic neural network not only produces a machine-learning-based fluid flow {surrogate} model but also systematically quantifies the uncertainty therein to assist with model interpretability.
This article presents an original methodology for the prediction of steady turbulent aerodynamic fields. Due to the important computational cost of high-fidelity aerodynamic simulations, a surrogate model is employed to cope with the significant variations of several inflow conditions. Specifically, the Local Decomposition Method presented in this paper has been derived to capture nonlinear behaviors resulting from the presence of continuous and discontinuous signals. A combination of unsupervised and supervised learning algorithms is coupled with a physical criterion. It decomposes automatically the input parameter space, from a limited number of high-fidelity simulations, into subspaces. These latter correspond to different flow regimes. A measure of entropy identifies the subspace with the expected strongest non-linear behavior allowing to perform an active resampling on this low-dimensional structure. Local reduced-order models are built on each subspace using Proper Orthogonal Decomposition coupled with a multivariate interpolation tool. The methodology is assessed on the turbulent two-dimensional flow around the RAE2822 transonic airfoil. It exhibits a significant improvement in term of prediction accuracy for the Local Decomposition Method compared with the classical method of surrogate modeling for cases with different flow regimes.
A two-fluid Discrete Boltzmann Model(DBM) for compressible flows based on Ellipsoidal Statistical Bhatnagar-Gross-Krook(ES-BGK) is presented. The model has flexible Prandtl number or specific heat ratio. Mathematically, the model is composed of two coupled Discrete Boltzmann Equations(DBE). Each DBE describes one component of the fluid. Physically, the model is equivalent to a macroscopic fluid model based on Navier-Stokes(NS) equations, and supplemented by a coarse-grained model for thermodynamic non-equilibrium behaviors. To obtain a flexible Prandtl number, a coefficient is introduced in the ellipsoidal statistical distribution function to control the viscosity. To obtain a flexible specific heat ratio, a parameter is introduced in the energy kinetic moments to control the extra degree of freedom. For binary mixture, the correspondence between the macroscopic fluid model and the DBM may be several-to-one. Five typical benchmark tests are used to verify and validate the model. Some interesting non-equilibrium results, which are not available in the NS model or the single-fluid DBM, are presented.
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