14,232 research outputs found
Predictive Reduced Order Modeling of Chaotic Multi-scale Problems Using Adaptively Sampled Projections
An adaptive projection-based reduced-order model (ROM) formulation is
presented for model-order reduction of problems featuring chaotic and
convection-dominant physics. An efficient method is formulated to adapt the
basis at every time-step of the on-line execution to account for the unresolved
dynamics. The adaptive ROM is formulated in a Least-Squares setting using a
variable transformation to promote stability and robustness. An efficient
strategy is developed to incorporate non-local information in the basis
adaptation, significantly enhancing the predictive capabilities of the
resulting ROMs. A detailed analysis of the computational complexity is
presented, and validated. The adaptive ROM formulation is shown to require
negligible offline training and naturally enables both future-state and
parametric predictions. The formulation is evaluated on representative reacting
flow benchmark problems, demonstrating that the ROMs are capable of providing
efficient and accurate predictions including those involving significant
changes in dynamics due to parametric variations, and transient phenomena. A
key contribution of this work is the development and demonstration of a
comprehensive ROM formulation that targets predictive capability in chaotic,
multi-scale, and transport-dominated problems
An adaptive, training-free reduced-order model for convection-dominated problems based on hybrid snapshots
The vast majority of reduced-order models (ROMs) first obtain a low
dimensional representation of the problem from high-dimensional model (HDM)
training data which is afterwards used to obtain a system of reduced
complexity. Unfortunately, convection-dominated problems generally have a
slowly decaying Kolmogorov n-width, which makes obtaining an accurate ROM built
solely from training data very challenging. The accuracy of a ROM can be
improved through enrichment with HDM solutions; however, due to the large
computational expense of HDM evaluations for complex problems, they can only be
used parsimoniously to obtain relevant computational savings. In this work, we
exploit the local spatial and temporal coherence often exhibited by these
problems to derive an accurate, cost-efficient approach that repeatedly
combines HDM and ROM evaluations without a separate training phase. Our
approach obtains solutions at a given time step by either fully solving the HDM
or by combining partial HDM and ROM solves. A dynamic sampling procedure
identifies regions that require the HDM solution for global accuracy and the
reminder of the flow is reconstructed using the ROM. Moreover, solutions
combining both HDM and ROM solves use spatial filtering to eliminate potential
spurious oscillations that may develop. We test the proposed method on inviscid
compressible flow problems and demonstrate speedups up to an order of
magnitude.Comment: 29 pages, 13 figure
Accelerated solutions of convection-dominated partial differential equations using implicit feature tracking and empirical quadrature
This work introduces an empirical quadrature-based hyperreduction procedure
and greedy training algorithm to effectively reduce the computational cost of
solving convection-dominated problems with limited training. The proposed
approach circumvents the slowly decaying -width limitation of linear model
reduction techniques applied to convection-dominated problems by using a
nonlinear approximation manifold systematically defined by composing a
low-dimensional affine space with bijections of the underlying domain. The
reduced-order model is defined as the solution of a residual minimization
problem over the nonlinear manifold. An online-efficient method is obtained by
using empirical quadrature to approximate the optimality system such that it
can be solved with mesh-independent operations. The proposed reduced-order
model is trained using a greedy procedure to systematically sample the
parameter domain. The effectiveness of the proposed approach is demonstrated on
two shock-dominated computational fluid dynamics benchmarks.Comment: 24 pages, 8 figures, 2 table
Registration-based model reduction of parameterized two-dimensional conservation laws
We propose a nonlinear registration-based model reduction procedure for rapid and reliable solution of parameterized two-dimensional steady conservation laws. This class of problems is challenging for model reduction techniques due to the presence of nonlinear terms in the equations and also due to the presence of parameter-dependent discontinuities that cannot be adequately represented through linear approximation spaces. Our approach builds on a general (i.e., independent of the underlying equation) registration procedure for the computation of a mapping Φ that tracks moving features of the solution field and on an hyper-reduced least-squares Petrov-Galerkin reduced-order model for the rapid and reliable computation of the solution coefficients. The contributions of this work are twofold. First, we investigate the application of registration-based methods to two-dimensional hyperbolic systems. Second, we propose a multi-fidelity approach to reduce the offline costs associated with the construction of the parameterized mapping and the reduced-order model. We discuss the application to an inviscid supersonic flow past a parameterized bump, to illustrate the many features of our method and to demonstrate its effectiveness
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