Application of deep learning method to Reynolds stress models of channel flow based on reduced-order modeling of DNS data

Key Words: Uncertainty Quantification, Deep Learning, Space-Time POD, Flood Modeling 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. 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. 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&#8217;s able to know what it knows, and more importantly, know when it doesn&#8217;t, which is still an open research area as far as neural networks are concerned [3]. REFERENCES [1] C. Szegedy, S. Ioffe, V. Vanhoucke, and A. A. Alemi, &#8220;Inception-v4, inception-resnet and the impact of residual connections on learning&#8221;, in Thirty-First AAAI Conference on Artificial Intelligence, 2017. [2] Q. Wang, J. S. Hesthaven, and D. Ray, &#8220;Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem&#8221;, Journal of Computational Physics, vol. 384, pp. 289&#8211;307, May 2019. [3] B. Lakshminarayanan, A. Pritzel, and C. Blundell, &#8220;Simple and scalable predictive uncertainty estimation using deep ensembles&#8221;, in Advances in Neural Information Processing Systems, 2017, pp. 6402&#8211;6413.

Download Full-text

Explicit algebraic subgrid stress models with application to rotating channel flow

Journal of Fluid Mechanics ◽

10.1017/s0022112009991054 ◽

2009 ◽

Vol 639 ◽

pp. 403-432 ◽

Cited By ~ 33

Author(s):

LINUS MARSTORP ◽

GEERT BRETHOUWER ◽

OLOF GRUNDESTAM ◽

ARNE V. JOHANSSON

Keyword(s):

Dynamic Model ◽

Reynolds Stress ◽

Channel Flow ◽

Stress Model ◽

Smagorinsky Model ◽

Mean Velocity ◽

The Mean ◽

Stress Models ◽

Subgrid Stress ◽

Rotating Channel

New explicit subgrid stress models are proposed involving the strain rate and rotation rate tensor, which can account for rotation in a natural way. The new models are based on the same methodology that leads to the explicit algebraic Reynolds stress model formulation for Reynolds-averaged Navier–Stokes simulations. One dynamic model and one non-dynamic model are proposed. The non-dynamic model represents a computationally efficient subgrid scale (SGS) stress model, whereas the dynamic model is the most accurate. The models are validated through large eddy simulations (LESs) of spanwise and streamwise rotating channel flow and are compared with the standard and dynamic Smagorinsky models. The proposed explicit dependence on the system rotation improves the description of the mean velocity profiles and the turbulent kinetic energy at high rotation rates. Comparison with the dynamic Smagorinsky model shows that not using the eddy-viscosity assumption improves the description of both the Reynolds stress anisotropy and the SGS stress anisotropy. LESs of rotating channel flow at Reτ = 950 have been carried out as well. These reveal some significant Reynolds number influences on the turbulence statistics. LESs of non-rotating turbulent channel flow at Reτ = 950 show that the new explicit model especially at coarse resolutions significantly better predicts the mean velocity, wall shear and Reynolds stresses than the dynamic Smagorinsky model, which is probably the result of a better prediction of the anisotropy of the subgrid dissipation.

Download Full-text

A deep learning enabler for nonintrusive reduced order modeling of fluid flows

Physics of Fluids ◽

10.1063/1.5113494 ◽

2019 ◽

Vol 31 (8) ◽

pp. 085101 ◽

Cited By ~ 23

Author(s):

S. Pawar ◽

S. M. Rahman ◽

H. Vaddireddy ◽

O. San ◽

A. Rasheed ◽

...

Keyword(s):

Deep Learning ◽

Fluid Flows ◽

Reduced Order Modeling ◽

Reduced Order

Download Full-text

A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs

Journal of Scientific Computing ◽

10.1007/s10915-021-01462-7 ◽

2021 ◽

Vol 87 (2) ◽

Cited By ~ 1

Author(s):

Stefania Fresca ◽

Luca Dede’ ◽

Andrea Manzoni

Keyword(s):

Deep Learning ◽

Reduced Order Modeling ◽

Time Dependent ◽

Reduced Basis ◽

Reduced Order ◽

Nonlinear Approach ◽

Parameter Values ◽

Proper Orthogonal ◽

Convection Dominated ◽

Very High

AbstractConventional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) may incur in severe limitations when dealing with nonlinear time-dependent parametrized PDEs, as these are strongly anchored to the assumption of modal linear superimposition they are based on. For problems featuring coherent structures that propagate over time such as transport, wave, or convection-dominated phenomena, the RB method may yield inefficient reduced order models (ROMs) when very high levels of accuracy are required. To overcome this limitation, in this work, we propose a new nonlinear approach to set ROMs by exploiting deep learning (DL) algorithms. In the resulting nonlinear ROM, which we refer to as DL-ROM, both the nonlinear trial manifold (corresponding to the set of basis functions in a linear ROM) as well as the nonlinear reduced dynamics (corresponding to the projection stage in a linear ROM) are learned in a non-intrusive way by relying on DL algorithms; the latter are trained on a set of full order model (FOM) solutions obtained for different parameter values. We show how to construct a DL-ROM for both linear and nonlinear time-dependent parametrized PDEs. Moreover, we assess its accuracy and efficiency on different parametrized PDE problems. Numerical results indicate that DL-ROMs whose dimension is equal to the intrinsic dimensionality of the PDE solutions manifold are able to efficiently approximate the solution of parametrized PDEs, especially in cases for which a huge number of POD modes would have been necessary to achieve the same degree of accuracy.

Download Full-text