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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.
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
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
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. Conseq
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 vari
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 c