scholarly journals Data-Targeted Prior Distribution for Variational AutoEncoder

Fluids ◽  
2021 ◽  
Vol 6 (10) ◽  
pp. 343
Author(s):  
Nissrine Akkari ◽  
Fabien Casenave ◽  
Thomas Daniel ◽  
David Ryckelynck
Keyword(s):  
Probability Distribution ◽  
Proper Orthogonal Decomposition ◽  
Prior Distribution ◽  
Posterior Probability ◽  
Fluid Flows ◽  
Velocity Fields ◽  
Orthogonal Decomposition ◽  
Training Data ◽  
Inference Model ◽  
Proper Orthogonal

Bayesian methods were studied in this paper using deep neural networks. We are interested in variational autoencoders, where an encoder approaches the true posterior and the decoder approaches the direct probability. Specifically, we applied these autoencoders for unsteady and compressible fluid flows in aircraft engines. We used inferential methods to compute a sharp approximation of the posterior probability of these parameters with the transient dynamics of the training velocity fields and to generate plausible velocity fields. An important application is the initialization of transient numerical simulations of unsteady fluid flows and large eddy simulations in fluid dynamics. It is known by the Bayes theorem that the choice of the prior distribution is very important for the computation of the posterior probability, proportional to the product of likelihood with the prior probability. Hence, we propose a new inference model based on a new prior defined by the density estimate with the realizations of the kernel proper orthogonal decomposition coefficients of the available training data. We numerically show that this inference model improves the results obtained with the usual standard normal prior distribution. This inference model was constructed using a new algorithm improving the convergence of the parametric optimization of the encoder probability distribution that approaches the posterior. This latter probability distribution is data-targeted, similarly to the prior distribution. This new generative approach can also be seen as an improvement of the kernel proper orthogonal decomposition method, for which we do not usually have a robust technique for expressing the pre-image in the input physical space of the stochastic reduced field in the feature high-dimensional space with a kernel inner product.

scholarly journals Construction of reduced-order models for fluid flows using deep feedforward neural networks

2019 ◽  
Vol 872 ◽  
pp. 963-994 ◽  
Author(s):  
Hugo F. S. Lui ◽  
William R. Wolf
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Fluid Flows ◽  
Leading Edge ◽  
Feedforward Neural Networks ◽  
Orthogonal Decomposition ◽  
Reduced Order Models ◽  
Order Model ◽  
Sparse Regression ◽  
Reduced Order ◽  
Proper Orthogonal

We present a numerical methodology for construction of reduced-order models (ROMs) of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition is applied to reduce the dimensionality of the model and, at the same time, filter the proper orthogonal decomposition temporal modes. The regression step is performed by a deep feedforward neural network (DNN), and the current framework is implemented in a context similar to the sparse identification of nonlinear dynamics algorithm. A discussion on the optimization of the DNN hyperparameters is provided for obtaining the best ROMs and an assessment of these models is presented for a canonical nonlinear oscillator and the compressible flow past a cylinder. Then the method is tested on the reconstruction of a turbulent flow computed by a large eddy simulation of a plunging airfoil under dynamic stall. The reduced-order model is able to capture the dynamics of the leading edge stall vortex and the subsequent trailing edge vortex. For the cases analysed, the numerical framework allows the prediction of the flow field beyond the training window using larger time increments than those employed by the full-order model. We also demonstrate the robustness of the current ROMs constructed via DNNs through a comparison with sparse regression. The DNN approach is able to learn transient features of the flow and presents more accurate and stable long-term predictions compared to sparse regression.

scholarly journals Convolutional-network models to predict wall-bounded turbulence from wall quantities

2021 ◽  
Vol 928 ◽  
Author(s):  
Luca Guastoni ◽  
Alejandro Güemes ◽  
Andrea Ianiro ◽  
Stefano Discetti ◽  
Philipp Schlatter ◽  
...  
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Reference Model ◽  
Orthogonal Decomposition ◽  
Training Data ◽  
Model Parameters ◽  
Convolutional Network ◽  
Loop Control ◽  
Fluctuation Fields ◽  
Proper Orthogonal ◽  
Wall Bounded Turbulence

Two models based on convolutional neural networks are trained to predict the two-dimensional instantaneous velocity-fluctuation fields at different wall-normal locations in a turbulent open-channel flow, using the wall-shear-stress components and the wall pressure as inputs. The first model is a fully convolutional neural network (FCN) which directly predicts the fluctuations, while the second one reconstructs the flow fields using a linear combination of orthonormal basis functions, obtained through proper orthogonal decomposition (POD), and is hence named FCN-POD. Both models are trained using data from direct numerical simulations at friction Reynolds numbers $Re_{\tau } = 180$ and 550. Being able to predict the nonlinear interactions in the flow, both models show better predictions than the extended proper orthogonal decomposition (EPOD), which establishes a linear relation between the input and output fields. The performance of the models is compared based on predictions of the instantaneous fluctuation fields, turbulence statistics and power-spectral densities. FCN exhibits the best predictions closer to the wall, whereas FCN-POD provides better predictions at larger wall-normal distances. We also assessed the feasibility of transfer learning for the FCN model, using the model parameters learned from the $Re_{\tau }=180$ dataset to initialize those of the model that is trained on the $Re_{\tau }=550$ dataset. After training the initialized model at the new $Re_{\tau }$ , our results indicate the possibility of matching the reference-model performance up to $y^{+}=50$ , with $50\,\%$ and $25\,\%$ of the original training data. We expect that these non-intrusive sensing models will play an important role in applications related to closed-loop control of wall-bounded turbulence.

Spatio-Temporal Analysis of Photospheric Turbulent Velocity Fields Using the Proper Orthogonal Decomposition

Solar Physics ◽  
2008 ◽  
Vol 251 (1-2) ◽  
pp. 163-178 ◽  
Author(s):  
A. Vecchio ◽  
V. Carbone ◽  
F. Lepreti ◽  
L. Primavera ◽  
L. Sorriso-Valvo ◽  
...  
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Temporal Analysis ◽  
Velocity Fields ◽  
Orthogonal Decomposition ◽  
Turbulent Velocity ◽  
Spatio Temporal ◽  
Proper Orthogonal

Proper Orthogonal Decomposition of HUSIR’s Temperature and Velocity Fields

2011 ◽  
Author(s):  
Kimberly H. Chung ◽  
Anthony A. DiCarlo
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Velocity Fields ◽  
Orthogonal Decomposition ◽  
Thermal Distortion ◽  
Design Consideration ◽  
Antenna Performance ◽  
W Band ◽  
Dynamics Models ◽  
Proper Orthogonal ◽  
Temperature And Velocity Fields

Thermal distortion is a critical design consideration for the Haystack Ultrawide-band Satellite Imaging Radar (HUSIR) with respect to its performance at W-band. This design consideration is needed due to the thermal distortion effects on the surface accuracy of a parabolic reflector. For example, a tight surface tolerance of ∼100 microns root-mean-squared is required to obtain 85 percent antenna performance efficiency for the 37 meter (120 foot) diameter reflector. An understanding of the temperature and velocity fields aids compensation of these losses. Computational fluid dynamics models (CFD) are too computationally expensive to implement in a control algorithm. Therefore, this work applies proper orthogonal decomposition (POD) to simulated CFD data and creates a reduced order model of the fluid system that characterizes the dominant features of both the temperature and velocity fields. A case study of the HUSIR’s convective flow inside a dome is illustrated.

scholarly journals A tale of two airfoils: resolvent-based modelling of an oscillator versus an amplifier from an experimental mean

2019 ◽  
Vol 881 ◽  
pp. 51-83 ◽  
Author(s):  
Sean Symon ◽  
Denis Sipp ◽  
Beverley J. McKeon
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Resolvent Operator ◽  
Stokes Equations ◽  
Velocity Fields ◽  
Orthogonal Decomposition ◽  
Low Rank ◽  
Experimental Measurements ◽  
Mean Velocity ◽  
Proper Orthogonal ◽  
The Resolvent Operator

The flows around a NACA 0018 airfoil at a chord-based Reynolds number of $Re=10\,250$ and angles of attack of $\unicode[STIX]{x1D6FC}=0^{\circ }$ and $\unicode[STIX]{x1D6FC}=10^{\circ }$ are modelled using resolvent analysis and limited experimental measurements obtained from particle image velocimetry. The experimental mean velocity fields are data assimilated so that they are solutions of the incompressible Reynolds-averaged Navier–Stokes equations forced by Reynolds stress terms which are derived from experimental data. Resolvent analysis of the data-assimilated mean velocity fields reveals low-rank behaviour only in the vicinity of the shedding frequency for $\unicode[STIX]{x1D6FC}=0^{\circ }$ and none of its harmonics. The resolvent operator for the $\unicode[STIX]{x1D6FC}=10^{\circ }$ case, on the other hand, identifies two linear mechanisms whose frequencies are a close match with those identified by spectral proper orthogonal decomposition. It is also shown that the second linear mechanism, corresponding to the Kelvin–Helmholtz instability in the shear layer, cannot be identified just by considering the time-averaged experimental measurements as an input for resolvent analysis due to missing data near the leading edge. For both cases, resolvent modes resemble those from spectral proper orthogonal decomposition when the resolvent operator is low rank. The $\unicode[STIX]{x1D6FC}=0^{\circ }$ case is classified as an oscillator and its harmonics, where the resolvent operator is not low rank, are modelled using parasitic modes as opposed to classical resolvent modes which are the most amplified. The $\unicode[STIX]{x1D6FC}=10^{\circ }$ case behaves more like an amplifier and its nonlinear forcing is far less structured. The two cases suggest that resolvent-based modelling can be achieved for more complex flows with limited experimental measurements.

scholarly journals Flow Structures Identification through Proper Orthogonal Decomposition: The Flow around Two Distinct Cylinders

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 384
Author(s):  
Ângela M. Ribau ◽  
Nelson D. Gonçalves ◽  
Luís L. Ferrás ◽  
Alexandre M. Afonso
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Fluid Flows ◽  
Orthogonal Decomposition ◽  
Flow Structures ◽  
Data Set ◽  
Power Law Fluids ◽  
2D Flow ◽  
Periodic Behaviour ◽  
Flow Through ◽  
Proper Orthogonal

Numerical simulations of fluid flows can produce a huge amount of data and inadvertently important flow structures can be ignored, if a thorough analysis is not performed. The identification of these flow structures, mainly in transient situations, is a complex task, since such structures change in time and can move along the domain. With the decomposition of the entire data set into smaller sets, important structures present in the main flow and structures with periodic behaviour, like vortices, can be identified. Therefore, through the analysis of the frequency of each of these components and using a smaller number of components, we show that the Proper Orthogonal Decomposition can be used not only to reduce the amount of significant data, but also to obtain a better and global understanding of the flow (through the analysis of specific modes). In this work, the von Kármán vortex street is decomposed into a generator base and analysed through the Proper Orthogonal Decomposition for the 2D flow around a cylinder and the 2D flow around two cylinders with different radii. We consider a Newtonian fluid and two non-Newtonian power-law fluids, with n=0.7 and n=1.3. Grouping specific modes, a reconstruction is made, allowing the identification of complex structures that otherwise would be impossible to identify using simple post-processing of the fluid flow.

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