Construction of reduced order models for fluid flows using deep neural networks Construção de modelos de ordem reduzida para escoamento de fluidos usando rede neurais profundas

2019 ◽  
Author(s):  
Hugo Felippe da Silva Lui
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Fluid Flows ◽  
Reduced Order Models ◽  
Reduced Order

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.

Design of microwave devices by segmentation, finite elements, reduced-order models, and neural networks

2007 ◽  
Vol 49 (3) ◽  
pp. 655-659
Author(s):  
Juan M. Cid ◽  
Jesús García ◽  
Javier Monge ◽  
Juan Zapata
Keyword(s):  
Neural Networks ◽  
Finite Elements ◽  
Microwave Devices ◽  
Reduced Order Models ◽  
Reduced Order

scholarly journals Reduced-Order Modeling of Deep Neural Networks

2021 ◽  
Vol 61 (5) ◽  
pp. 774-785
Author(s):  
J. Gusak ◽  
T. Daulbaev ◽  
E. Ponomarev ◽  
A. Cichocki ◽  
I. Oseledets
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Reduced Order Modeling ◽  
Reduced Order

scholarly journals POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium

2021 ◽  
Vol 12 ◽  
Author(s):  
Stefania Fresca ◽  
Andrea Manzoni ◽  
Luca Dedè ◽  
Alfio Quarteroni
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Left Atrium ◽  
Real Time ◽  
Cardiac Electrophysiology ◽  
Front Propagation ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Training Costs ◽  
Speed Up

The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) for parametrized PDEs to speed up the solution of the aforementioned problems can be problematic. This is primarily due to the strong variability characterizing the solution set and to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To enhance ROM efficiency, we proposed a new generation of non-intrusive, nonlinear ROMs, based on deep learning (DL) algorithms, such as convolutional, feedforward, and autoencoder neural networks. In the proposed DL-ROM, both the nonlinear solution manifold and the nonlinear reduced dynamics used to model the system evolution on that manifold can be learnt in a non-intrusive way thanks to DL algorithms trained on a set of FOM snapshots. DL-ROMs were shown to be able to accurately capture complex front propagation processes, both in physiological and pathological cardiac EP, very rapidly once neural networks were trained, however, at the expense of huge training costs. In this study, we show that performing a prior dimensionality reduction on FOM snapshots through randomized proper orthogonal decomposition (POD) enables to speed up training times and to decrease networks complexity. Accuracy and efficiency of this strategy, which we refer to as POD-DL-ROM, are assessed in the context of cardiac EP on an idealized left atrium (LA) geometry and considering snapshots arising from a NURBS (non-uniform rational B-splines)-based isogeometric analysis (IGA) discretization. Once the ROMs have been trained, POD-DL-ROMs can efficiently solve both physiological and pathological cardiac EP problems, for any new scenario, in real-time, even in extremely challenging contexts such as those featuring circuit re-entries, that are among the factors triggering cardiac arrhythmias.

scholarly journals Long-time Reynolds averaging of reduced order models for fluid flows: Preliminary results

2020 ◽  
Vol 2 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Luigi C. Berselli ◽  
◽  
Traian Iliescu ◽  
Birgul Koc ◽  
Roger Lewandowski ◽  
...  
Keyword(s):  
Fluid Flows ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Preliminary Results ◽  
Long Time ◽  
Reynolds Averaging

Reduced-Order Flood Modeling Using Uncertainty-Aware Deep Neural Networks

2020 ◽  
Author(s):  
Pierre Jacquier ◽  
Azzedine Abdedou ◽  
Azzeddine Soulaïmani
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Uncertainty Quantification ◽  
Surrogate Model ◽  
Deep Neural Networks ◽  
Reduced Order Modeling ◽  
Flood Modeling ◽  
Reduced Order ◽  
Highly Nonlinear ◽  
The Impact

<p><strong>Key Words</strong>: Uncertainty Quantification, Deep Learning, Space-Time POD, Flood Modeling</p><p><br>While impressive results have been achieved in the well-known fields where Deep Learning allowed for breakthroughs such as computer vision, language modeling, or content generation [1], its impact on different, older fields is still vastly unexplored. In computational fluid dynamics and especially in Flood Modeling, many phenomena are very high-dimensional, and predictions require the use of finite element or volume methods, which can be, while very robust and tested, computational-heavy and may not prove useful in the context of real-time predictions. This led to various attempts at developing Reduced-Order Modeling techniques, both intrusive and non-intrusive. One late relevant addition was a combination of Proper Orthogonal Decomposition with Deep Neural Networks (POD-NN) [2]. Yet, to our knowledge, in this example and more generally in the field, little work has been conducted on quantifying uncertainties through the surrogate model.<br>In this work, we aim at comparing different novel methods addressing uncertainty quantification in reduced-order models, pushing forward the POD-NN concept with ensembles, latent-variable models, as well as encoder-decoder models. These are tested on benchmark problems, and then applied to a real-life application: flooding predictions in the Mille-Iles river in Laval, QC, Canada.<br>For the flood modeling application, our setup involves a set of input parameters resulting from onsite measures. High-fidelity solutions are then generated using our own finite-volume code CuteFlow, which is solving the highly nonlinear Shallow Water Equations. The goal is then to build a non-intrusive surrogate model, that’s able to <em>know what it know</em>s, and more importantly, <em>know when it doesn’t</em>, which is still an open research area as far as neural networks are concerned [3].</p><p><br><strong>REFERENCES</strong><br>[1] C. Szegedy, S. Ioffe, V. Vanhoucke, and A. A. Alemi, “Inception-v4, inception-resnet and the impact of residual connections on learning”, in Thirty-First AAAI Conference on Artificial Intelligence, 2017.<br>[2] Q. Wang, J. S. Hesthaven, and D. Ray, “Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem”, Journal of Computational Physics, vol. 384, pp. 289–307, May 2019.<br>[3] B. Lakshminarayanan, A. Pritzel, and C. Blundell, “Simple and scalable predictive uncertainty estimation using deep ensembles”, in Advances in Neural Information Processing Systems, 2017, pp. 6402–6413.</p>

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