Reduced-order modelling of parameterised incompressible and compressible unsteady flow problems using deep neural networks

2021 ◽  
Vol 66 (1) ◽  
pp. 36
Author(s):  
Oliviu Şugar Gabor
Keyword(s):  
Neural Networks ◽  
Unsteady Flow ◽  
Deep Neural Networks ◽  
Reduced Order ◽  
Flow Problems ◽  
Reduced Order Modelling

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

Reduced Order Model for Unsteady Fluid Flows via Recurrent Neural Networks

2019 ◽  
Author(s):  
Sandeep B. Reddy ◽  
Allan Ross Magee ◽  
Rajeev K. Jaiman ◽  
J. Liu ◽  
W. Xu ◽  
...  
Keyword(s):  
Neural Networks ◽  
Reynolds Number ◽  
Flow Field ◽  
Unsteady Flow ◽  
Recurrent Neural Networks ◽  
Reduced Order Model ◽  
Data Driven ◽  
Order Model ◽  
Reduced Order ◽  
Low Dimensional

Abstract In this paper, we present a data-driven approach to construct a reduced-order model (ROM) for the unsteady flow field and fluid-structure interaction. This proposed approach relies on (i) a projection of the high-dimensional data from the Navier-Stokes equations to a low-dimensional subspace using the proper orthogonal decomposition (POD) and (ii) integration of the low-dimensional model with the recurrent neural networks. For the hybrid ROM formulation, we consider long short term memory networks with encoder-decoder architecture, which is a special variant of recurrent neural networks. The mathematical structure of recurrent neural networks embodies a non-linear state space form of the underlying dynamical behavior. This particular attribute of an RNN makes it suitable for non-linear unsteady flow problems. In the proposed hybrid RNN method, the spatial and temporal features of the unsteady flow system are captured separately. Time-invariant modes obtained by low-order projection embodies the spatial features of the flow field, while the temporal behavior of the corresponding modal coefficients is learned via recurrent neural networks. The effectiveness of the proposed method is first demonstrated on a canonical problem of flow past a cylinder at low Reynolds number. With regard to a practical marine/offshore engineering demonstration, we have applied and examined the reliability of the proposed data-driven framework for the predictions of vortex-induced vibrations of a flexible offshore riser at high Reynolds number.

scholarly journals Deep learning or interpolation for inverse modelling of heat and fluid flow problems?

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Rainald Löhner ◽  
Harbir Antil ◽  
Hamid Tamaddon-Jahromi ◽  
Neeraj Kavan Chakshu ◽  
Perumal Nithiarasu
Keyword(s):  
Neural Networks ◽  
Heat Conduction ◽  
Deep Neural Networks ◽  
Nonlinear Behaviour ◽  
Content Type ◽  
Flow Problems ◽  
Interpolation Algorithms ◽  
Transfer Problems ◽  
First Time ◽  
Heat And Fluid Flow

Purpose The purpose of this study is to compare interpolation algorithms and deep neural networks for inverse transfer problems with linear and nonlinear behaviour. Design/methodology/approach A series of runs were conducted for a canonical test problem. These were used as databases or “learning sets” for both interpolation algorithms and deep neural networks. A second set of runs was conducted to test the prediction accuracy of both approaches. Findings The results indicate that interpolation algorithms outperform deep neural networks in accuracy for linear heat conduction, while the reverse is true for nonlinear heat conduction problems. For heat convection problems, both methods offer similar levels of accuracy. Originality/value This is the first time such a comparison has been made.

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>

scholarly journals Physics‐Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems

2020 ◽  
Vol 56 (5) ◽  
Author(s):  
A. M. Tartakovsky ◽  
C. Ortiz Marrero ◽  
Paris Perdikaris ◽  
G. D. Tartakovsky ◽  
D. Barajas‐Solano
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Subsurface Flow ◽  
Flow Problems ◽  
Constitutive Relationships
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