63 research outputs found
Data-driven sub-grid model development for large eddy simulations of turbulence
Turbulence modeling remains an active area of research due to its significant impact on a diverse set of challenges such as those pertaining to the aerospace and geophysical communities. Researchers continue to search for modeling strategies that improve the representation of high-wavenumber content in practical computational fluid dynamics applications. The recent successes of machine learning in the physical sciences have motivated a number of studies into the modeling of turbulence from a data-driven point of view. In this research, we utilize physics-informed machine learning to reconstruct the effect of unresolved frequencies (i.e., small-scale turbulence) on grid-resolved flow-variables obtained through large eddy simulation. In general, it is seen that the successful development of any data-driven strategy relies on two phases - learning and a-posteriori deployment. The former requires the synthesis of labeled data from direct numerical simulations of our target phenomenon whereas the latter requires the development of stability preserving modifications instead of a direct deployment of learning predictions. These stability preserving techniques may be through prediction modulation - where learning outputs are deployed via an intermediate statistical truncation. They may also be through the utilization of model classifiers where the traditional -minimization strategy is avoided for a categorical cross-entropy error which flags for the most stable model deployment at a point on the computational grid. In this thesis, we outline several investigations utilizing the aforementioned philosophies and come to the conclusion that sub-grid turbulence models built through the utilization of machine learning are capable of recovering viable statistical trends in stabilized a-posteriori deployments for Kraichnan and Kolmogorov turbulence. Therefore, they represent a promising tool for the generation of closures that may be utilized in flows that belong to different configurations and have different sub-grid modeling requirements
Interpretable Fine-Tuning for Graph Neural Network Surrogate Models
Data-based surrogate modeling has surged in capability in recent years with
the emergence of graph neural networks (GNNs), which can operate directly on
mesh-based representations of data. The goal of this work is to introduce an
interpretable fine-tuning strategy for GNNs, with application to unstructured
mesh-based fluid dynamics modeling. The end result is a fine-tuned GNN that
adds interpretability to a pre-trained baseline GNN through an adaptive
sub-graph sampling strategy that isolates regions in physical space
intrinsically linked to the forecasting task, while retaining the predictive
capability of the baseline. The structures identified by the fine-tuned GNNs,
which are adaptively produced in the forward pass as explicit functions of the
input, serve as an accessible link between the baseline model architecture, the
optimization goal, and known problem-specific physics. Additionally, through a
regularization procedure, the fine-tuned GNNs can also be used to identify,
during inference, graph nodes that correspond to a majority of the anticipated
forecasting error, adding a novel interpretable error-tagging capability to
baseline models. Demonstrations are performed using unstructured flow data
sourced from flow over a backward-facing step at high Reynolds numbers
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
- …