14 research outputs found
Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations
This paper introduces tensorial calculus techniques in the framework of
Proper Orthogonal Decomposition (POD) to reduce the computational complexity of
the reduced nonlinear terms. The resulting method, named tensorial POD, can be
applied to polynomial nonlinearities of any degree . Such nonlinear terms
have an on-line complexity of , where is the
dimension of POD basis, and therefore is independent of full space dimension.
However it is efficient only for quadratic nonlinear terms since for higher
nonlinearities standard POD proves to be less time consuming once the POD basis
dimension is increased. Numerical experiments are carried out with a two
dimensional shallow water equation (SWE) test problem to compare the
performance of tensorial POD, standard POD, and POD/Discrete Empirical
Interpolation Method (DEIM). Numerical results show that tensorial POD
decreases by times the computational cost of the on-line stage of
standard POD for configurations using more than model variables. The
tensorial POD SWE model was only slower than the POD/DEIM SWE model
but the implementation effort is considerably increased. Tensorial calculus was
again employed to construct a new algorithm allowing POD/DEIM shallow water
equation model to compute its off-line stage faster than the standard and
tensorial POD approaches.Comment: 23 pages, 8 figures, 5 table
Memory embedded non-intrusive reduced order modeling of non-ergodic flows
Generating a digital twin of any complex system requires modeling and
computational approaches that are efficient, accurate, and modular. Traditional
reduced order modeling techniques are targeted at only the first two but the
novel non-intrusive approach presented in this study is an attempt at taking
all three into account effectively compared to their traditional counterparts.
Based on dimensionality reduction using proper orthogonal decomposition (POD),
we introduce a long short-term memory (LSTM) neural network architecture
together with a principal interval decomposition (PID) framework as an enabler
to account for localized modal deformation, which is a key element in accurate
reduced order modeling of convective flows. Our applications for convection
dominated systems governed by Burgers, Navier-Stokes, and Boussinesq equations
demonstrate that the proposed approach yields significantly more accurate
predictions than the POD-Galerkin method, and could be a key enabler towards
near real-time predictions of unsteady flows
CAMERA: A Method for Cost-aware, Adaptive, Multifidelity, Efficient Reliability Analysis
Estimating probability of failure in aerospace systems is a critical
requirement for flight certification and qualification. Failure probability
estimation involves resolving tails of probability distribution, and Monte
Carlo sampling methods are intractable when expensive high-fidelity simulations
have to be queried. We propose a method to use models of multiple fidelities
that trade accuracy for computational efficiency. Specifically, we propose the
use of multifidelity Gaussian process models to efficiently fuse models at
multiple fidelity, thereby offering a cheap surrogate model that emulates the
original model at all fidelities. Furthermore, we propose a novel sequential
\emph{acquisition function}-based experiment design framework that can
automatically select samples from appropriate fidelity models to make
predictions about quantities of interest in the highest fidelity. We use our
proposed approach in an importance sampling setting and demonstrate our method
on the failure level set estimation and probability estimation on synthetic
test functions as well as two real-world applications, namely, the reliability
analysis of a gas turbine engine blade using a finite element method and a
transonic aerodynamic wing test case using Reynolds-averaged Navier--Stokes
equations. We demonstrate that our method predicts the failure boundary and
probability more accurately and computationally efficiently while using varying
fidelity models compared with using just a single expensive high-fidelity
model.Comment: 35 page, 16 figure
Sensitivity to Large-Scale Environmental Fields of the Relaxed Arakawa-Schubert Parameterization in the Nasa GEOS-1 GCM
This article is organized as follows. In Section 2, we briefly describe the theory and algorithm of adjoint sensitivity studies. Section 3 presents the result of the sensitivity analyses, and conclusions are drawn in Section 4
Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows
Reduced rank nonlinear filters are increasingly utilized in data assimilation of geophysical flows but often require a set of ensemble forward simulations to estimate forecast covariance. On the other hand, predictor–corrector type nudging approaches are still attractive due to their simplicity of implementation when more complex methods need to be avoided. However, optimal estimate of the nudging gain matrix might be cumbersome. In this paper, we put forth a fully nonintrusive recurrent neural network approach based on a long short-term memory (LSTM) embedding architecture to estimate the nudging term, which plays a role not only to force the state trajectories to the observations but also acts as a stabilizer. Furthermore, our approach relies on the power of archival data, and the trained model can be retrained effectively due to the power of transfer learning in any neural network applications. In order to verify the feasibility of the proposed approach, we perform twin experiments using the Lorenz 96 system. Our results demonstrate that the proposed LSTM nudging approach yields more accurate estimates than both the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) when only sparse observations are available. With the availability of emerging artificial intelligence friendly and modular hardware technologies and heterogeneous computing platforms, we articulate that our simplistic nudging framework turns out to be computationally more efficient than either the EKF or EnKF approaches