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Efficient non-linear model reduction via a least-squares Petrov–Galerkin projection and compressive tensor approximations
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In this article, the authors acknowledge the partial support of the National Science Foundation Graduate Fellowship and the National Defense Science and Engineering Graduate Fellowship for a research grant from King Abdullah University of Science and Technology (KAUST) and Stanford University.Abstract:
The first author acknowledges the partial support by a National Science Foundation Graduate Fellowship and the partial support by a National Defense Science and Engineering Graduate Fellowship. The second and third authors acknowledge the partial support by the Motor Sports Division of the Toyota Motor Corporation under Agreement Number 48737, and the partial support by a research grant from the Academic Excellence Alliance program between King Abdullah University of Science and Technology (KAUST) and Stanford University. All authors also acknowledge the constructive comments received during the review process.read more
Citations
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Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
TL;DR: In many situations across computational science and engineering, multiple computational models are available that describe a system of interest as discussed by the authors, and these different models have varying evaluation costs, i.e.
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Isogeometric finite element data structures based on Bézier extraction of T-splines
Michael A. Scott,Michael J. Borden,Michael J. Borden,Clemens V. Verhoosel,Thomas W. Sederberg,Thomas J. R. Hughes +5 more
TL;DR: It is shown that the extraction operator and Bézier elements provide an element structure for isogeometric analysis that can be easily incorporated into existing finite element codes, without any changes to element form and assembly algorithms, and standard data processing arrays.
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The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows
TL;DR: Global state-space error bounds are developed that justify the method's design and highlight its advantages in terms of minimizing components of these error bounds and a 'sample mesh' concept is introduced that enables a distributed, computationally efficient implementation of the GNAT method in finite-volume-based computational-fluid-dynamics (CFD) codes.
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TL;DR: In this paper, the authors bring together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science, and highlight many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy.
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Closed-Loop Turbulence Control: Progress and Challenges
Steven L. Brunton,Bernd R. Noack +1 more
References
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Book
Iterative Methods for Sparse Linear Systems
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Book
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
TL;DR: In this article, the authors present a review of rigor properties of low-dimensional models and their applications in the field of fluid mechanics. But they do not consider the effects of random perturbation on models.
Book
Approximation of Large-Scale Dynamical Systems
TL;DR: This paper presents SVD-Krylov Methods and Case Studies, a monograph on model reduction using Krylov methods for linear dynamical systems, and some examples of such reduction schemes.