Near-Wall Turbulence Modeling using Neural Networks
Abstract not provided.
Publications
Machine-Learned Models for Near-Wall Turbulence
Abstract not provided.
Coordinate-Invariant Near-Wall Turbulence Modeling via Neural Networks
Abstract not provided.
Near-wall modeling using coordinate frame invariant representations and neural networks
AIAA Aviation 2019 Forum
Near-wall turbulence models in Large-Eddy Simulation (LES) typically approximate near-wall behavior using a solution to the mean flow equations. This approach inevitably leads to errors when the modeled flow does not satisfy the assumptions surrounding the use of a mean flow approximation for an unsteady boundary condition. Herein, modern machine learning (ML) techniques are utilized to implement a coordinate frame invariant model of the wall shear stress that is derived specifically for complex flows for which mean near-wall models are known to fail. The model operates on a set of scalar and vector invariants based on data taken from the first LES grid point off the wall. Neural networks were trained and validated on spatially filtered direct numerical simulation (DNS) data. The trained networks were then tested on data to which they were never previously exposed and comparisons of the accuracy of the networks’ predictions of wall-shear stress were made to both a standard mean wall model approach and to the true stress values taken from the DNS data. The ML approach showed considerable improvement in both the accuracy of individual shear stress predictions as well as produced a more accurate distribution of wall shear stress values than did the standard mean wall model. This result held both in regions where the standard mean approach typically performs satisfactorily as well as in regions where it is known to fail, and also in cases where the networks were trained and tested on data taken from the same flow type/region as well as when trained and tested on data from different respective flow topologies.
Turbulent Flow UQ Using Machine Learning Techniques
Abstract not provided.
Multifidelity uncertainty quantification using spectral stochastic discrepancy models
Handbook of Uncertainty Quantification
When faced with a restrictive evaluation budget that is typical of today's highfidelity simulation models, the effective exploitation of lower-fidelity alternatives within the uncertainty quantification (UQ) process becomes critically important. Herein, we explore the use of multifidelity modeling within UQ, for which we rigorously combine information from multiple simulation-based models within a hierarchy of fidelity, in seeking accurate high-fidelity statistics at lower computational cost. Motivated by correction functions that enable the provable convergence of a multifidelity optimization approach to an optimal high-fidelity point solution, we extend these ideas to discrepancy modeling within a stochastic domain and seek convergence of a multifidelity uncertainty quantification process to globally integrated high-fidelity statistics. For constructing stochastic models of both the low-fidelity model and the model discrepancy, we employ stochastic expansion methods (non-intrusive polynomial chaos and stochastic collocation) computed by integration/interpolation on structured sparse grids or regularized regression on unstructured grids. We seek to employ a coarsely resolved grid for the discrepancy in combination with a more finely resolved Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. Grid for the low-fidelity model. The resolutions of these grids may be defined statically or determined through uniform and adaptive refinement processes. Adaptive refinement is particularly attractive, as it has the ability to preferentially target stochastic regions where the model discrepancy becomes more complex, i.e., where the predictive capabilities of the low-fidelity model start to break down and greater reliance on the high-fidelity model (via the discrepancy) is necessary. These adaptive refinement processes can either be performed separately for the different grids or within a coordinated multifidelity algorithm. In particular, we present an adaptive greedy multifidelity approach in which we extend the generalized sparse grid concept to consider candidate index set refinements drawn from multiple sparse grids, as governed by induced changes in the statistical quantities of interest and normalized by relative computational cost. Through a series of numerical experiments using statically defined sparse grids, adaptive multifidelity sparse grids, and multifidelity compressed sensing, we demonstrate that the multifidelity UQ process converges more rapidly than a single-fidelity UQ in cases where the variance of the discrepancy is reduced relative to the variance of the high-fidelity model (resulting in reductions in initial stochastic error), where the spectrum of the expansion coefficients of the model discrepancy decays more rapidly than that of the high-fidelity model (resulting in accelerated convergence rates), and/or where the discrepancy is more sparse than the high-fidelity model (requiring the recovery of fewer significant terms).
Machine Learning Models of Errors in LES Predictions of Surface Pressure Fluctuations
Abstract not provided.
Machine Learning Models of Errors in Large Eddy Simulation Predictions of Surface Pressure Fluctuations
Abstract not provided.
Convolutional Neural Networks for Frequency Response Predictions
Abstract not provided.
Approaches for building stable projection-based reduced order models for compressible flow
Abstract not provided.
Investigating Turbulent Wall Pressure Fluctuations using Machine Learning Techniques
Abstract not provided.
Development of machine learning models for turbulent wall pressure fluctuations
AIAA SciTech Forum - 55th AIAA Aerospace Sciences Meeting
In many aerospace applications, it is critical to be able to model fluid-structure interactions. In particular, correctly predicting the power spectral density of pressure fluctuations at surfaces can be important for assessing potential resonances and failure modes. Current turbulence modeling methods, such as wall-modeled Large Eddy Simulation and Detached Eddy Simulation, cannot reliably predict these pressure fluctuations for many applications of interest. The focus of this paper is on efforts to use data-driven machine learning methods to learn correction terms for the wall pressure fluctuation spectrum. In particular, the non-locality of the wall pressure fluctuations in a compressible boundary layer is investigated using random forests and neural networks trained and evaluated on Direct Numerical Simulation data.
Development of Machine Learning Models for Turbulent Wall Pressure Fluctuations
Abstract not provided.
Development of Machine Learning Models for Turbulent Wall Pressure Fluctuations
Abstract not provided.
Stabilization of Projection-Based Reduced Order Models via Optimization-Based Eigenvalue Reassignment
Abstract not provided.
Construction of energy-stable projection-based reduced order models
Applied Mathematics and Computation
An approach for building energy-stable Galerkin reduced order models (ROMs) for linear hyperbolic or incompletely parabolic systems of partial differential equations (PDEs) using continuous projection is developed. This method is an extension of earlier work by the authors specific to the equations of linearized compressible inviscid flow. The key idea is to apply to the PDEs a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. For linear problems, the desired transformation is induced by a special inner product, termed the "symmetry inner product", which is derived herein for several systems of physical interest. Connections are established between the proposed approach and other stability-preserving model reduction methods, giving the paper a review flavor. More specifically, it is shown that a discrete counterpart of this inner product is a weighted L2 inner product obtained by solving a Lyapunov equation, first proposed by Rowley et al. and termed herein the "Lyapunov inner product". Comparisons between the symmetry inner product and the Lyapunov inner product are made, and the performance of ROMs constructed using these inner products is evaluated on several benchmark test cases.
Energy-Stable Galerkin Reduced Order Models for Nonlinear Compressible Flow
Abstract not provided.
Multi-Fidelity Uncertainty Quantification: Application to a Vertical Axis Wind Turbine Under an Extreme Gust
Abstract not provided.
Reduced Order Modeling for Prediction and Control of Large-Scale Systems
This report describes work performed from June 2012 through May 2014 as a part of a Sandia Early Career Laboratory Directed Research and Development (LDRD) project led by the first author. The objective of the project is to investigate methods for building stable and efficient proper orthogonal decomposition (POD)/Galerkin reduced order models (ROMs): models derived from a sequence of high-fidelity simulations but having a much lower computational cost. Since they are, by construction, small and fast, ROMs can enable real-time simulations of complex systems for onthe- spot analysis, control and decision-making in the presence of uncertainty. Of particular interest to Sandia is the use of ROMs for the quantification of the compressible captive-carry environment, simulated for the design and qualification of nuclear weapons systems. It is an unfortunate reality that many ROM techniques are computationally intractable or lack an a priori stability guarantee for compressible flows. For this reason, this LDRD project focuses on the development of techniques for building provably stable projection-based ROMs. Model reduction approaches based on continuous as well as discrete projection are considered. In the first part of this report, an approach for building energy-stable Galerkin ROMs for linear hyperbolic or incompletely parabolic systems of partial differential equations (PDEs) using continuous projection is developed. The key idea is to apply a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. It is shown that, for many PDE systems including the linearized compressible Euler and linearized compressible Navier-Stokes equations, the desired transformation is induced by a special inner product, termed the “symmetry inner product”. Attention is then turned to nonlinear conservation laws. A new transformation and corresponding energy-based inner product for the full nonlinear compressible Navier-Stokes equations is derived, and it is demonstrated that if a Galerkin ROM is constructed in this inner product, the ROM system energy will be bounded in a way that is consistent with the behavior of the exact solution to these PDEs, i.e., the ROM will be energy-stable. The viability of the linear as well as nonlinear continuous projection model reduction approaches developed as a part of this project is evaluated on several test cases, including the cavity configuration of interest in the targeted application area. In the second part of this report, some POD/Galerkin approaches for building stable ROMs using discrete projection are explored. It is shown that, for generic linear time-invariant (LTI) systems, a discrete counterpart of the continuous symmetry inner product is a weighted L2 inner product obtained by solving a Lyapunov equation. This inner product was first proposed by Rowley et al., and is termed herein the “Lyapunov inner product“. Comparisons between the symmetry inner product and the Lyapunov inner product are made, and the performance of ROMs constructed using these inner products is evaluated on several benchmark test cases. Also in the second part of this report, a new ROM stabilization approach, termed “ROM stabilization via optimization-based eigenvalue reassignment“, is developed for generic LTI systems. At the heart of this method is a constrained nonlinear least-squares optimization problem that is formulated and solved numerically to ensure accuracy of the stabilized ROM. Numerical studies reveal that the optimization problem is computationally inexpensive to solve, and that the new stabilization approach delivers ROMs that are stable as well as accurate. Summaries of “lessons learned“ and perspectives for future work motivated by this LDRD project are provided at the end of each of the two main chapters.
Stabilized projection-based reduced order models for uncertainty quantification
Abstract not provided.
Stabilization of Projection-Based Reduced Order Models via Eigenvalue Reassignment
Computer Methods in Applied Mechanics and Engineering
Abstract not provided.
Stabilization of Projection-Based Reduced Order Models via Optimization-Based Eigenvalue Reassignment
CMAME
Abstract not provided.
Construction of energy-stable Galerkin reduced order models
This report aims to unify several approaches for building stable projection-based reduced order models (ROMs). Attention is focused on linear time-invariant (LTI) systems. The model reduction procedure consists of two steps: the computation of a reduced basis, and the projection of the governing partial differential equations (PDEs) onto this reduced basis. Two kinds of reduced bases are considered: the proper orthogonal decomposition (POD) basis and the balanced truncation basis. The projection step of the model reduction can be done in two ways: via continuous projection or via discrete projection. First, an approach for building energy-stable Galerkin ROMs for linear hyperbolic or incompletely parabolic systems of PDEs using continuous projection is proposed. The idea is to apply to the set of PDEs a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. The resulting ROM will be energy-stable for any choice of reduced basis. It is shown that, for many PDE systems, the desired transformation is induced by a special weighted L2 inner product, termed the %E2%80%9Csymmetry inner product%E2%80%9D. Attention is then turned to building energy-stable ROMs via discrete projection. A discrete counterpart of the continuous symmetry inner product, a weighted L2 inner product termed the %E2%80%9CLyapunov inner product%E2%80%9D, is derived. The weighting matrix that defines the Lyapunov inner product can be computed in a black-box fashion for a stable LTI system arising from the discretization of a system of PDEs in space. It is shown that a ROM constructed via discrete projection using the Lyapunov inner product will be energy-stable for any choice of reduced basis. Connections between the Lyapunov inner product and the inner product induced by the balanced truncation algorithm are made. Comparisons are also made between the symmetry inner product and the Lyapunov inner product. The performance of ROMs constructed using these inner products is evaluated on several benchmark test cases.
Advances in UQ Algorithms for Wind Energy Applications
Abstract not provided.
Large-Scale Uncertainty and Error Analysis for Time-dependent Fluid/Structure Interactions in Wind Turbine Applications: Summary of Advances in Algorithm Research and Deployment
Abstract not provided.
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