2,573 research outputs found
Sub-grid modelling for two-dimensional turbulence using neural networks
In this investigation, a data-driven turbulence closure framework is
introduced and deployed for the sub-grid modelling of Kraichnan turbulence. The
novelty of the proposed method lies in the fact that snapshots from
high-fidelity numerical data are used to inform artificial neural networks for
predicting the turbulence source term through localized grid-resolved
information. In particular, our proposed methodology successfully establishes a
map between inputs given by stencils of the vorticity and the streamfunction
along with information from two well-known eddy-viscosity kernels. Through this
we predict the sub-grid vorticity forcing in a temporally and spatially dynamic
fashion. Our study is both a-priori and a-posteriori in nature. In the former,
we present an extensive hyper-parameter optimization analysis in addition to
learning quantification through probability density function based validation
of sub-grid predictions. In the latter, we analyse the performance of our
framework for flow evolution in a classical decaying two-dimensional turbulence
test case in the presence of errors related to temporal and spatial
discretization. Statistical assessments in the form of angle-averaged kinetic
energy spectra demonstrate the promise of the proposed methodology for sub-grid
quantity inference. In addition, it is also observed that some measure of
a-posteriori error must be considered during optimal model selection for
greater accuracy. The results in this article thus represent a promising
development in the formalization of a framework for generation of
heuristic-free turbulence closures from data
Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables
Fast Neural Network Predictions from Constrained Aerodynamics Datasets
Incorporating computational fluid dynamics in the design process of jets,
spacecraft, or gas turbine engines is often challenged by the required
computational resources and simulation time, which depend on the chosen
physics-based computational models and grid resolutions. An ongoing problem in
the field is how to simulate these systems faster but with sufficient accuracy.
While many approaches involve simplified models of the underlying physics,
others are model-free and make predictions based only on existing simulation
data. We present a novel model-free approach in which we reformulate the
simulation problem to effectively increase the size of constrained pre-computed
datasets and introduce a novel neural network architecture (called a cluster
network) with an inductive bias well-suited to highly nonlinear computational
fluid dynamics solutions. Compared to the state-of-the-art in model-based
approximations, we show that our approach is nearly as accurate, an order of
magnitude faster, and easier to apply. Furthermore, we show that our method
outperforms other model-free approaches
RANS Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned
Reynolds-averaged Navier--Stokes (RANS) simulations with turbulence closure
models continue to play important roles in industrial flow simulations.
However, the commonly used linear eddy viscosity models are intrinsically
unable to handle flows with non-equilibrium turbulence. Reynolds stress models,
on the other hand, are plagued by their lack of robustness. Recent studies in
plane channel flows found that even substituting Reynolds stresses with errors
below 0.5% from direct numerical simulation (DNS) databases into RANS equations
leads to velocities with large errors (up to 35%). While such an observation
may have only marginal relevance to traditional Reynolds stress models, it is
disturbing for the recently emerging data-driven models that treat the Reynolds
stress as an explicit source term in the RANS equations, as it suggests that
the RANS equations with such models can be ill-conditioned. So far, a rigorous
analysis of the condition of such models is still lacking. As such, in this
work we propose a metric based on local condition number function for a priori
evaluation of the conditioning of the RANS equations. We further show that the
ill-conditioning cannot be explained by the global matrix condition number of
the discretized RANS equations. Comprehensive numerical tests are performed on
turbulent channel flows at various Reynolds numbers and additionally on two
complex flows, i.e., flow over periodic hills and flow in a square duct.
Results suggest that the proposed metric can adequately explain observations in
previous studies, i.e., deteriorated model conditioning with increasing
Reynolds number and better conditioning of the implicit treatment of Reynolds
stress compared to the explicit treatment. This metric can play critical roles
in the future development of data-driven turbulence models by enforcing the
conditioning as a requirement on these models.Comment: 35 pages, 18 figure
Machine Learning for Fluid Mechanics
The field of fluid mechanics is rapidly advancing, driven by unprecedented
volumes of data from field measurements, experiments and large-scale
simulations at multiple spatiotemporal scales. Machine learning offers a wealth
of techniques to extract information from data that could be translated into
knowledge about the underlying fluid mechanics. Moreover, machine learning
algorithms can augment domain knowledge and automate tasks related to flow
control and optimization. This article presents an overview of past history,
current developments, and emerging opportunities of machine learning for fluid
mechanics. It outlines fundamental machine learning methodologies and discusses
their uses for understanding, modeling, optimizing, and controlling fluid
flows. The strengths and limitations of these methods are addressed from the
perspective of scientific inquiry that considers data as an inherent part of
modeling, experimentation, and simulation. Machine learning provides a powerful
information processing framework that can enrich, and possibly even transform,
current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202
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