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

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

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

Leveraging the structure of dynamical systems for data-driven modeling

The reliable prediction of the temporal behavior of complex systems is required in numerous scientific fields. This strong interest is however hindered by modeling issues: often, the governing equations describing the physics of the system under consideration are not accessible or, when known, their solution might require a computational time incompatible with the prediction time constraints. Nowadays, approximating complex systems at hand in a generic functional format and informing it ex--nihilo from available observations has become a common practice, as illustrated by the enormous amount of scientific work appeared in the last years. Numerous successful examples based on deep neural networks are already available, although generalizability of the models and margins of guarantee are often overlooked. Here, we consider Long-Short Term Memory neural networks and thoroughly investigate the impact of the training set and its structure on the quality of the long-term prediction. Leveraging insights from ergodic theory, we perform a thorough computational analysis to assess the amount of data sufficient for a priori guaranteeing a faithful model of the physical system. We show how an informed design of the training set, based on invariants of the system and the structure of the underlying attractor, significantly improves the resulting models, opening up avenues for research within the context of active learning. Further, the non-trivial effects of the memory initializations when relying on memory-capable models will be illustrated. Our findings provide evidence-based good-practice on the amount and the choice of data required for an effective data-driven modeling of any complex dynamical system

Closed-loop optimal control for shear flows using reinforcement learning

International audienc

Modélisation par termes source de générateurs de vortex pour le contrôle d'écoulement : Validations expérimentales et optimisations

Cette étude porte sur la manipulation d'écoulement à l'aide de VG. Pour limiter la taille des maillages dans les simulations numériques, la géométrie des VG n'est pas explicitement représentée: les VG sont modélisés par des termes sources incorporés aux équations de quantité de mouvement. Nous présentons ici la validation de cette modélisation par des mesures expérimentales et des simulations avec des VG maillés sur une configuration de plaque plane. Une optimisation des paramètres de forme des VG est ensuite menée suivant différentes méthodes en comparant le coût calcul

Continuous Methods : Hamiltonian Domain Translation

This paper proposes a novel approach to domain translation. Leveraging established parallels between generative models and dynamical systems, we propose a reformulation of the Cycle-GAN architecture. By embedding our model with a Hamiltonian structure, we obtain a continuous, expressive and most importantly invertible generative model for domain translation