Дисертації з теми "Data-driven model order reduction"
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Quaranta, Giacomo. "Efficient simulation tools for real-time monitoring and control using model order reduction and data-driven techniques." Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/667474.
Повний текст джерелаLa simulación numérica, el uso de ordenadores para ejecutar un programa que implementa un modelo matemático de un sistema físico, es una parte importante del mundo tecnológico actual. En muchos campos de la ciencia y la ingeniería es necesario estudiar el comportamiento de sistemas cuyos modelos matemáticos son demasiado complejos para proporcionar soluciones analíticas, haciendo posible la evaluación virtual de las respuestas de los sistemas (gemelos virtuales). Esto reduce drásticamente el número de pruebas experimentales para los diseños precisos del sistema real que el modelo numérico representa. Sin embargo, estos gemelos virtuales, basados en métodos clásicos que hacen uso de una rica representación del sistema (por ejemplo, el método de elementos finitos), rara vez permiten la retroalimentación en tiempo real, incluso cuando se considera la computación en plataformas de alto rendimiento. En estas circunstancias, el rendimiento en tiempo real requerido en algunas aplicaciones se ve comprometido. En efecto, los gemelos virtuales son estáticos, es decir, se utilizan en el diseño de sistemas complejos y sus componentes, pero no se espera que acomoden o asimilen los datos para definir sistemas de aplicación dinámicos basados en datos. Además, se suelen apreciar desviaciones significativas entre la respuesta observada y la predicha por el modelo, debido a inexactitudes en los modelos empleados, en la determinación de los parámetros del modelo o en su evolución temporal. En esta tesis se proponen diferentes métodos para resolver estas limitaciones con el fin de realizar un seguimiento y un control en tiempo real. En la primera parte se utilizan técnicas de Reducción de Modelos para satisfacer las restricciones en tiempo real; estas técnicas calculan una buena aproximación de la solución simplificando el procedimiento de resolución en lugar del modelo. La precisión de la solución no se ve comprometida y se pueden realizar simulaciones efficientes (gemelos digitales). En la segunda parte se emplea la modelización basada en datos para llenar el vacío entre la solución paramétrica, calculada utilizando técnicas de reducción de modelos no intrusivas, y los campos medidos, con el fin de hacer posibles los sistemas de aplicación dinámicos basados en datos (gemelos híbridos).
La simulation numérique, c'est-à-dire l'utilisation des ordinateurs pour exécuter un programme qui met en oeuvre un modèle mathématique d'un système physique, est une partie importante du monde technologique actuel. Elle est nécessaire dans de nombreux domaines scientifiques et techniques pour étudier le comportement de systèmes dont les modèles mathématiques sont trop complexes pour fournir des solutions analytiques et elle rend possible l'évaluation virtuelle des réponses des systèmes (jumeaux virtuels). Cela réduit considérablement le nombre de tests expérimentaux nécessaires à la conception précise du système réel que le modèle numérique représente. Cependant, ces jumeaux virtuels, basés sur des méthodes classiques qui utilisent une représentation fine du système (ex. méthode des éléments finis), permettent rarement une rétroaction en temps réel, même dans un contexte de calcul haute performance, fonctionnant sur des plates-formes puissantes. Dans ces circonstances, les performances en temps réel requises dans certaines applications sont compromises. En effet, les jumeaux virtuels sont statiques, c'est-à-dire qu'ils sont utilisés dans la conception de systèmes complexes et de leurs composants, mais on ne s'attend pas à ce qu'ils prennent en compte ou assimilent des données afin de définir des systèmes d'application dynamiques pilotés par les données. De plus, des écarts significatifs entre la réponse observée et celle prévue par le modèle sont généralement constatés en raison de l'imprécision des modèles employés, de la détermination des paramètres du modèle ou de leur évolution dans le temps. Dans cette thèse, nous proposons di érentes méthodes pour résoudre ces handicaps afin d'effectuer une surveillance et un contrôle en temps réel. Dans la première partie, les techniques de Réduction de Modèles sont utilisées pour tenir compte des contraintes en temps réel ; elles calculent une bonne approximation de la solution en simplifiant la procédure de résolution plutôt que le modèle. La précision de la solution n'est pas compromise et des simulations e caces peuvent être réalisées (jumeaux numériquex). Dans la deuxième partie, la modélisation pilotée par les données est utilisée pour combler l'écart entre la solution paramétrique calculée, en utilisant des techniques de réduction de modèles non intrusives, et les champs mesurés, afin de rendre possibles des systèmes d'application dynamiques basés sur les données (jumeaux hybrides).
Ibañez, Pinillo Ruben. "Advanced physics-based and data-driven strategies." Thesis, Ecole centrale de Nantes, 2019. http://www.theses.fr/2019ECDN0021.
Повний текст джерелаSimulation Based Engineering Science (SBES) has brought major improvements in optimization, control and inverse analysis, all leading to a deeper understanding in many processes occurring in the real world. These noticeable breakthroughs are present in a vast variety of sectors such as aeronautic or automotive industries, mobile telecommunications or healthcare among many other fields. Nevertheless, SBES is currently confronting several difficulties to provide accurate results in complex industrial problems. Apart from the high computational costs associated with industrial applications, the errors introduced by constitutive modeling become more and more important when dealing with new materials. Concurrently, an unceasingly growing interest in concepts such as Big-Data, Machine Learning or Data-Analytics has been experienced. Indeed, this interest is intrinsically motivated by an exhaustive development in both dataacquisition and data-storage systems. For instance, an aircraft may produce over 500 GB of data during a single flight. This panorama brings a perfect opportunity to the socalled Dynamic Data Driven Application Systems (DDDAS), whose main objective is to merge classical simulation algorithms with data coming from experimental measures in a dynamic way. Within this scenario, data and simulations would no longer be uncoupled but rather a symbiosis that is to be exploited would achieve milestones which were inconceivable until these days. Indeed, data will no longer be understood as a static calibration of a given constitutive model but rather the model will be corrected dynamically as soon as experimental data and simulations tend to diverge. Several numerical algorithms will be presented throughout this manuscript whose main objective is to strengthen the link between data and computational mechanics. The first part of the thesis is mainly focused on parameter identification, data-driven and data completion techniques. The second part is focused on Model Order Reduction (MOR) techniques, since they constitute a fundamental ally to achieve real time constraints arising from DDDAS framework
Waseem, Abdullah. "Numerical Homogenization and Model Reduction for Transient Heat, Diffusion and coupled Mechanics Problems." Thesis, Ecole centrale de Nantes, 2020. http://www.theses.fr/2020ECDN0028.
Повний текст джерелаIn this thesis computationally efficient numerical homogenization techniques are presented for diffusion phenomena in heterogeneous materials. As a preliminary step, a model reduction for the transient heat diffusion equation is performed at the micro-scale using component mode synthesis, which provides an emergent enriched-continuum description at the macro-scale. Based on the location of the enrichmentvariables, either on the finite element nodes or the quadrature points, two spatial discretization schemes are analyzed for the enrichedcontinuum. The proposed model reduction is also extended to the transient mass diffusion coupled to the mechanics with application to lithium-ion batteries. Chemical potential and strain fields formulation is used which allows the use of standard C0-continuous finite elements. The micro-scale problem, which usually involves an expensive solution of the coupled mass diffusionmechanics problem is now replaced by a set of ordinary differential equations through model reduction. Finally, an alternative model reduction approach using data-driven mechanics is explored. It relies on a direct search and interpolation from a database instead of the solution of a microscopic problem. The database is constructed and stored using the microscopic calculations in an offline stage. It also provides a route to extend the proposed model reduction method to the nonlinear regime
Taddei, Tommaso. "Model order reduction methods for data assimilation : state estimation and structural health monitoring." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/108942.
Повний текст джерелаCataloged from PDF version of thesis.
Includes bibliographical references (pages 243-258).
The objective of this thesis is to develop and analyze model order reduction approaches for the efficient integration of parametrized mathematical models and experimental measurements. Model Order Reduction (MOR) techniques for parameterized Partial Differential Equations (PDEs) offer new opportunities for the integration of models and experimental data. First, MOR techniques speed up computations allowing better explorations of the parameter space. Second, MOR provides actionable tools to compress our prior knowledge about the system coming from the parameterized best-knowledge model into low-dimensional and more manageable forms. In this thesis, we demonstrate how to take advantage of MOR to design computational methods for two classes of problems in data assimilation. In the first part of the thesis, we discuss and extend the Parametrized-Background Data-Weak (PBDW) approach for state estimation. PBDW combines a parameterized best knowledge mathematical model and experimental data to rapidly estimate the system state over the domain of interest using a small number of local measurements. The approach relies on projection-by-data, and exploits model reduction techniques to encode the knowledge of the parametrized model into a linear space appropriate for real-time evaluation. In this work, we extend the PBDW formulation in three ways. First, we develop an experimental a posteriori estimator for the error in the state. Second, we develop computational procedures to construct local approximation spaces in subregions of the computational domain in which the best-knowledge model is defined. Third, we present an adaptive strategy to handle experimental noise in the observations. We apply our approach to a companioni heat transfer experiment to prove the effectiveness of our technique. In the second part of the thesis, we present a model-order reduction approach to simulation based classification, with particular application to Structural Health Monitoring (SHM). The approach exploits (i) synthetic results obtained by repeated solution of a parametrized PDE for different values of the parameters, (ii) machine-learning algorithms to generate a classifier that monitors the state of damage of the system, and (iii) a reduced basis method to reduce the computational burden associated with the model evaluations. The approach is based on an offline/online computational decomposition. In the offline stage, the fields associated with many different system configurations, corresponding to different states of damage, are computed and then employed to teach a classifier. Model reduction techniques, ideal for this many-query context, are employed to reduce the computational burden associated with the parameter exploration. In the online stage, the classifier is used to associate measured data to the relevant diagnostic class. In developing our approach for SHM, we focus on two specific aspects. First, we develop a mathematical formulation which properly integrates the parameterized PDE model within the classification problem. Second, we present a sensitivity analysis to take into account the error in the model. We illustrate our method and we demonstrate its effectiveness through the vehicle of a particular companion experiment, a harmonically excited microtruss.
by Tommaso Taddei.
Ph. D.
Lauzeral, Nathan. "Reduced order and sparse representations for patient-specific modeling in computational surgery." Thesis, Ecole centrale de Nantes, 2019. http://www.theses.fr/2019ECDN0062.
Повний текст джерелаThis thesis investigates the use of model order reduction methods based on sparsity-related techniques for the development of real-time biophysical modeling. In particular, it focuses on the embedding of interactive biophysical simulation into patient-specific models of tissues and organs to enhance medical images and assist the clinician in the process of informed decision making. In this context, three fundamental bottlenecks arise. The first lies in the embedding of the shape parametrization into the parametric reduced order model to faithfully represent the patient’s anatomy. A non-intrusive approach relying on a sparse sampling of the space of anatomical features is introduced and validated. Then, we tackle the problem of data completion and image reconstruction from partial or incomplete datasets based on physical priors. The proposed solution has the potential to perform scene registration in the context of augmented reality for laparoscopy. Quasi-real-time computations are reached by using a new hyperreduction approach based on a sparsity promoting technique. Finally, the third challenge concerns the representation of biophysical systems under uncertainty of the underlying parameters. It is shown that traditional model order reduction approaches are not always successful in producing a low dimensional representation of a model, in particular in the case of electrosurgery simulation. An alternative is proposed using a metamodeling approach. To this end, we successfully extend the use of sparse regression methods to the case of systems with stochastic parameters
Akhtar, Sabina. "Vérification Formelle d'Algorithmes Distribués en PlusCal-2." Phd thesis, Université de Lorraine, 2012. http://tel.archives-ouvertes.fr/tel-00815570.
Повний текст джерелаKoc, Birgul. "Numerical Analysis for Data-Driven Reduced Order Model Closures." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/103202.
Повний текст джерелаDoctor of Philosophy
In many realistic applications, obtaining an accurate approximation to a given problem can require a tremendous number of degrees of freedom. Solving these large systems of equations can take days or even weeks on standard computational platforms. Thus, lower-dimensional models, i.e., reduced order models (ROMs), are often used instead. The ROMs are computationally efficient and accurate when the underlying system has dominant and recurrent spatial structures. Our contribution to reduced order modeling is adding a data-driven correction term, which carries important information and yields better ROM approximations. This dissertation's theoretical and numerical results show that the new ROM equipped with a closure term yields more accurate approximations than the standard ROM.
Hammond, Janelle K. "Méthodes des bases réduites pour la modélisation de la qualité de l'air urbaine." Thesis, Paris Est, 2017. http://www.theses.fr/2017PESC1230/document.
Повний текст джерелаThe principal objective of this thesis is the development of low-cost numerical tools for spatial mapping of pollutant concentrations from field observations and advanced deterministic models. With increased pollutant emissions and exposure due to mass urbanization and development worldwide, air quality measurement campaigns and epidemiology studies of the association between air pollution and adverse health effects have become increasingly common. However, as air pollution concentrations are highly variable spatially and temporally, the sensitivity and accuracy of these epidemiology studies is often deteriorated by exposure misclassi cation due to poor estimates of individual exposures. Data assimilation methods incorporate available measurement data and mathematical models to provide improved approximations of the concentration. These methods, when based on an advanced deterministic air quality models (AQMs), could provide spatially-rich small-scale approximations and can enable better estimates of effects and exposures. However, these methods can be computationally expensive. They require repeated solution of the model, which could itself be costly. In this work we investigate a combined reduced basis (RB) data assimilation method for use with advanced AQMs on urban scales. We want to diminish the cost of resolution, using RB arguments, and incorporate measurement data to improve the quality of the solution. We extend the Parameterized-Background Data-Weak (PBDW) method to physically-based AQMs. This method can rapidly estimate "online" pollutant concentrations at urban scale, using available AQMs in a non-intrusive and computationally effcient manner, reducing computation times by factors up to hundreds. We apply this method in case studies representing urban residential pollution of PM2.5, and we study the stability of the method depending on the placement or air quality sensors. Results from the PBDW are compared to the Generalized Empirical Interpolation Method (GEIM) and a standard inverse problem, the adjoint method, in order to measure effciency of the method. This comparison shows possible improvement in precision and great improvement in computation cost with respect to classical methods. We fi nd that the PBDW method shows promise for the real-time reconstruction of a pollution eld in large-scale problems, providing state estimation with approximation error generally under 10% when applied to an imperfect model
Ulin, Samuel. "Digging deep : A data-driven approach to model reduction in a granular bulldozing scenario." Thesis, Umeå universitet, Institutionen för fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-152498.
Повний текст джерелаSavas, Berkant. "Algorithms in data mining using matrix and tensor methods." Doctoral thesis, Linköpings universitet, Beräkningsvetenskap, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11597.
Повний текст джерелаWang, Jianxun. "Physics-Informed, Data-Driven Framework for Model-Form Uncertainty Estimation and Reduction in RANS Simulations." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/77035.
Повний текст джерелаPh. D.
Grimm, Alexander Rudolf. "Parametric Dynamical Systems: Transient Analysis and Data Driven Modeling." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/83840.
Повний текст джерелаPh. D.
Fahlaoui, Tarik. "Réduction de modèles et apprentissage de solutions spatio-temporelles paramétrées à partir de données : application à des couplages EDP-EDO." Thesis, Compiègne, 2020. http://www.theses.fr/2020COMP2535.
Повний текст джерелаIn this thesis, an algorithm for learning an accurate reduced order model from data generated by a high fidelity solver (HF solver) is proposed. To achieve this goal, we use both Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD). Anomaly detection, during the learning process, can be easily done by performing an a posteriori spectral analysis on the reduced order model learnt. Several extensions are presented to make the method as general as possible. Thus, we handle the case of coupled ODE/PDE systems or the case of second order hyperbolic equations. The method is also extended to the case of switched control systems, where the switching rule is learnt by using an Artificial Neural Network (ANN). The reduced order model learnt allows to predict time evolution of the POD coefficients. However, the POD coefficients have no interpretable meaning. To tackle this issue, we propose an interpretable reduction method using the Empirical Interpolation Method (EIM). This reduction method is then adapted to the case of third-order tensors, and combining with the Kernel Ridge Regression (KRR) we can learn the solution manifold in the case of parametrized PDEs. In this way, we can learn a parametrized reduced order model. The case of non-linear PDEs or disturbed data is finally presented in the opening
Boubehziz, Toufik. "Simulation en quasi temps réel d’une capsule sous écoulement grâce à des Modèles d’Ordre Réduit." Thesis, Compiègne, 2022. http://www.theses.fr/2022COMP2678.
Повний текст джерелаThe motion of a liquid-filled microcapsule flowing in a microchannel is a complex problem tosimulate. Two innovative reduced-order data-driven models are proposed to replace the Fluid Structure Interaction (FSI) model using a collected database from high-fidelity simulations. The objective is to replace the existing Full Order Model (FOM) with a fast-simulation model that can simulate the capsule deformation in flow at a low cost in terms of time and calculation. The first model consists in building from a space-time-parameter datacube a reduced model to simulate the deformation of the microcapsule for any admissible configuration of parameters. Time evolution of the capsule deformation is treated by identifying the nonlinear low-order manifold of the reduced variables. Then, manifold learning is applied using the Diffuse Approximation (DA) method to predict capsule deformation for a query configuration of parameters and a chosen time discretization. The second model is based on rewriting the FSI model under the form of a reduced-order dynamic system. In this latter, the spectral displacement and velocity coefficients are related through a dynamic operator to be identified. To determine this operator, we suggest the use of a dynamic mode decomposition approach. Numerical validations prove the reliability and stability of the two new models compared to the high order model. A software application has been developed to explore the capsule deformation evolution for any couple of admissible parameters
Xie, Xuping. "Large Eddy Simulation Reduced Order Models." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/77626.
Повний текст джерелаPh. D.
Zavar, Moosavi Azam Sadat. "Probabilistic and Statistical Learning Models for Error Modeling and Uncertainty Quantification." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/82491.
Повний текст джерелаPh. D.
Lestandi, Lucas. "Approximations de rang faible et modèles d'ordre réduit appliqués à quelques problèmes de la mécanique des fluides." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0186/document.
Повний текст джерелаNumerical simulation has experienced tremendous improvements in the last decadesdriven by massive growth of computing power. Exascale computing has beenachieved this year and will allow solving ever more complex problems. But suchlarge systems produce colossal amounts of data which leads to its own difficulties.Moreover, many engineering problems such as multiphysics or optimisation andcontrol, require far more power that any computer architecture could achievewithin the current scientific computing paradigm. In this thesis, we proposeto shift the paradigm in order to break the curse of dimensionality byintroducing decomposition and building reduced order models (ROM) for complexfluid flows.This manuscript is organized into two parts. The first one proposes an extendedreview of data reduction techniques and intends to bridge between appliedmathematics community and the computational mechanics one. Thus, foundingbivariate separation is studied, including discussions on the equivalence ofproper orthogonal decomposition (POD, continuous framework) and singular valuedecomposition (SVD, discrete matrices). Then a wide review of tensor formats andtheir approximation is proposed. Such work has already been provided in theliterature but either on separate papers or into a purely applied mathematicsframework. Here, we offer to the data enthusiast scientist a comparison ofCanonical, Tucker, Hierarchical and Tensor train formats including theirapproximation algorithms. Their relative benefits are studied both theoreticallyand numerically thanks to the python library texttt{pydecomp} that wasdeveloped during this thesis. A careful analysis of the link between continuousand discrete methods is performed. Finally, we conclude that for mostapplications ST-HOSVD is best when the number of dimensions $d$ lower than fourand TT-SVD (or their POD equivalent) when $d$ grows larger.The second part is centered on a complex fluid dynamics flow, in particular thesingular lid driven cavity at high Reynolds number. This flow exhibits a seriesof Hopf bifurcation which are known to be hard to capture accurately which iswhy a detailed analysis was performed both with classical tools and POD. Oncethis flow has been characterized, emph{time-scaling}, a new ``physics based''interpolation ROM is presented on internal and external flows. This methodsgives encouraging results while excluding recent advanced developments in thearea such as EIM or Grassmann manifold interpolation
Gstalter, Étienne. "Réduction d’ordre de modèle de crash automobile pour l’optimisation masse / prestations." Thesis, Compiègne, 2020. http://www.theses.fr/2020COMP2576.
Повний текст джерелаThis thesis is a part of a global research work dedicated to reduced-order modelling applications in the Renault engineering direction. It's research topic has been improved in the IRT System)('s project on Reduced Order Model and Multi-disciplinary Optimization. Some previous thesis can help understand the context. ([Vuong], [Charrier]). The main industrial application of the research theme is the focus on a body structure, in a crash loading. Some research works on acoustic, combustion and aerodynamic are currently ongoing. This thesis is both a contribution to the generic ReCUR method, and its application to a car body structure optimization for crash loadings. Engineering teams at Renault uses optimization to obtain the best crash simulation, with a numerical optimization software, based on designs of experiments. It requires a lot of crash simulation because each simulation is considered as unique, with only one response for each parameter. Only Inputs and Outputs are known. The ReCUR method consider that each simulation is a huge mine that needs our attention. We hope that we can decrease the number of crash simulation required to compute a model, by using much more data for each simulation
Li, He. "Second-order Least Squares Estimation in Generalized Linear Mixed Models." 2011. http://hdl.handle.net/1993/4446.
Повний текст джерела