629 research outputs found
Randomized Dynamic Mode Decomposition
This paper presents a randomized algorithm for computing the near-optimal
low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging
techniques to compute low-rank matrix approximations at a fraction of the cost
of deterministic algorithms, easing the computational challenges arising in the
area of `big data'. The idea is to derive a small matrix from the
high-dimensional data, which is then used to efficiently compute the dynamic
modes and eigenvalues. The algorithm is presented in a modular probabilistic
framework, and the approximation quality can be controlled via oversampling and
power iterations. The effectiveness of the resulting randomized DMD algorithm
is demonstrated on several benchmark examples of increasing complexity,
providing an accurate and efficient approach to extract spatiotemporal coherent
structures from big data in a framework that scales with the intrinsic rank of
the data, rather than the ambient measurement dimension. For this work we
assume that the dynamics of the problem under consideration is evolving on a
low-dimensional subspace that is well characterized by a fast decaying singular
value spectrum
Streakline-based closed-loop control of a bluff body flow
A novel closed-loop control methodology is introduced to stabilize a cylinder wake flow based on images of streaklines. Passive scalar tracers are injected upstream the cylinder and their concentration is monitored downstream at certain image sectors of the wake. An AutoRegressive with eXogenous inputs mathematical model is built from these images and a Generalized Predictive Controller algorithm is used to compute the actuation required to stabilize the wake by adding momentum tangentially to the cylinder wall through plasma actuators. The methodology is new and has real-world applications. It is demonstrated on a numerical simulation and the provided results show that good performances are achieved.Fil: Roca, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Ingeniería Mecánica. Laboratorio de Fluidodinámica; ArgentinaFil: Cammilleri, Ada. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Ingeniería Mecánica. Laboratorio de Fluidodinámica; ArgentinaFil: Duriez, Thomas Pierre Cornil. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Ingeniería Mecánica. Laboratorio de Fluidodinámica; ArgentinaFil: Mathelin, Lionel. Centre National de la Recherche Scientifique. Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur; FranciaFil: Artana, Guillermo Osvaldo. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Ingeniería Mecánica. Laboratorio de Fluidodinámica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
A dynamic mode decomposition approach for large and arbitrarily sampled systems
Detection of coherent structures is of crucial importance for understanding the dynamics of a fluid flow. In this regard, the recently introduced Dynamic Mode Decomposition (DMD) has raised an increasing interest in the community. It allows to efficiently determine the dominant spatial modes, and their associated growth rate andfrequencyintime,responsiblefordescribingthetime-evolutionofanobservation ofthephysicalsystemathand.However,theunderlyingalgorithmrequiresuniformly sampled and time-resolved data, which may limit its usability in practical situations. Further, the computational cost associated with the DMD analysis of a large dataset is high, both in terms of central processing unit and memory. In this contribution, we present an alternative algorithm to achieve this decomposition, overcoming the above-mentioned limitations. A synthetic case, a two-dimensional restriction of an experimental flow over an open cavity, and a large-scale three-dimensional simulation, provide examples to illustrate the method
Sparse approximation of multivariate functions from small datasets via weighted orthogonal matching pursuit
We show the potential of greedy recovery strategies for the sparse
approximation of multivariate functions from a small dataset of pointwise
evaluations by considering an extension of the orthogonal matching pursuit to
the setting of weighted sparsity. The proposed recovery strategy is based on a
formal derivation of the greedy index selection rule. Numerical experiments
show that the proposed weighted orthogonal matching pursuit algorithm is able
to reach accuracy levels similar to those of weighted minimization
programs while considerably improving the computational efficiency for small
values of the sparsity level
Discrepancy-Based Active Learning for Domain Adaptation
The goal of the paper is to design active learning strategies which lead to
domain adaptation under an assumption of covariate shift in the case of
Lipschitz labeling function. Building on previous work by Mansour et al. (2009)
we adapt the concept of discrepancy distance between source and target
distributions to restrict the maximization over the hypothesis class to a
localized class of functions which are performing accurate labeling on the
source domain. We derive generalization error bounds for such active learning
strategies in terms of Rademacher average and localized discrepancy for general
loss functions which satisfy a regularity condition. A practical K-medoids
algorithm that can address the case of large data set is inferred from the
theoretical bounds. Our numerical experiments show that the proposed algorithm
is competitive against other state-of-the-art active learning techniques in the
context of domain adaptation, in particular on large data sets of around one
hundred thousand images.Comment: 28 pages, 11 figure
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