1,137 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
MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework
We propose MeshfreeFlowNet, a novel deep learning-based super-resolution
framework to generate continuous (grid-free) spatio-temporal solutions from the
low-resolution inputs. While being computationally efficient, MeshfreeFlowNet
accurately recovers the fine-scale quantities of interest. MeshfreeFlowNet
allows for: (i) the output to be sampled at all spatio-temporal resolutions,
(ii) a set of Partial Differential Equation (PDE) constraints to be imposed,
and (iii) training on fixed-size inputs on arbitrarily sized spatio-temporal
domains owing to its fully convolutional encoder. We empirically study the
performance of MeshfreeFlowNet on the task of super-resolution of turbulent
flows in the Rayleigh-Benard convection problem. Across a diverse set of
evaluation metrics, we show that MeshfreeFlowNet significantly outperforms
existing baselines. Furthermore, we provide a large scale implementation of
MeshfreeFlowNet and show that it efficiently scales across large clusters,
achieving 96.80% scaling efficiency on up to 128 GPUs and a training time of
less than 4 minutes.Comment: Supplementary Video: https://youtu.be/mjqwPch9gDo. Accepted to SC2
A posteriori learning for quasi-geostrophic turbulence parametrization
The use of machine learning to build subgrid parametrizations for climate
models is receiving growing attention. State-of-the-art strategies address the
problem as a supervised learning task and optimize algorithms that predict
subgrid fluxes based on information from coarse resolution models. In practice,
training data are generated from higher resolution numerical simulations
transformed in order to mimic coarse resolution simulations. By essence, these
strategies optimize subgrid parametrizations to meet so-called criteria. But the actual purpose of a subgrid parametrization is to
obtain good performance in terms of metrics which imply
computing entire model trajectories. In this paper, we focus on the
representation of energy backscatter in two dimensional quasi-geostrophic
turbulence and compare parametrizations obtained with different learning
strategies at fixed computational complexity. We show that strategies based on
criteria yield parametrizations that tend to be unstable in
direct simulations and describe how subgrid parametrizations can alternatively
be trained end-to-end in order to meet criteria. We
illustrate that end-to-end learning strategies yield parametrizations that
outperform known empirical and data-driven schemes in terms of performance,
stability and ability to apply to different flow configurations. These results
support the relevance of differentiable programming paradigms for climate
models in the future.Comment: 36 pages, 14 figures, submitted to Journal of Advances in Modeling
Earth Systems (JAMES
A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence
In the present study, we investigate different data-driven parameterizations
for large eddy simulation of two-dimensional turbulence in the \emph{a priori}
settings. These models utilize resolved flow field variables on the coarser
grid to estimate the subgrid-scale stresses. We use data-driven closure models
based on localized learning that employs multilayer feedforward artificial
neural network (ANN) with point-to-point mapping and neighboring stencil data
mapping, and convolutional neural network (CNN) fed by data snapshots of the
whole domain. The performance of these data-driven closure models is measured
through a probability density function and is compared with the dynamic
Smagorinksy model (DSM). The quantitative performance is evaluated using the
cross-correlation coefficient between the true and predicted stresses. We
analyze different frameworks in terms of the amount of training data, selection
of input and output features, their characteristics in modeling with accuracy,
and training and deployment computational time. We also demonstrate
computational gain that can be achieved using the intelligent eddy viscosity
model that learns eddy viscosity computed by the DSM instead of subgrid-scale
stresses. We detail the hyperparameters optimization of these models using the
grid search algorithm
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