## Search

Now showing items 1-10 of 65

JavaScript is disabled for your browser. Some features of this site may not work without it.

AuthorTempone, Raul (20)Alouini, Mohamed-Slim (9)Bagci, Hakan (9)Nobile, Fabio (7)Litvinenko, Alexander (5)View MoreDepartmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE) (55)Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (51)Applied Mathematics and Computational Science Program (24)Electrical Engineering Program (18)Physical Sciences and Engineering (PSE) Division (6)View MorePublisherKAUST SRI UQ (1)SubjectApplications (10)Sampling (9)CEM (8)Low-Rank (7)Wireless (7)View MoreTypePoster (50)Presentation (14)Meetings and Proceedings (1)Year (Issue Date)2014 (65)Item AvailabilityOpen Access (65)

Now showing items 1-10 of 65

- List view
- Grid view
- Sort Options:
- Relevance
- Title Asc
- Title Desc
- Issue Date Asc
- Issue Date Desc
- Submit Date Asc
- Submit Date Desc
- Results Per Page:
- 5
- 10
- 20
- 40
- 60
- 80
- 100

Collocation methods for uncertainty quanti cation in PDE models with random data

Nobile, Fabio (2014-01-06) [Presentation]

In this talk we consider Partial Differential Equations (PDEs) whose input data are modeled as random fields to account for their intrinsic variability or our lack of knowledge. After parametrizing the input random fields by finitely many independent random variables, we exploit the high regularity of the solution of the PDE as a function of the input random variables and consider sparse polynomial approximations in probability (Polynomial Chaos expansion) by collocation methods. We first address interpolatory approximations where the PDE is solved on a sparse grid of Gauss points in the probability space and the solutions thus obtained interpolated by multivariate polynomials. We present recent results on optimized sparse grids in which the selection of points is based on a knapsack approach and relies on sharp estimates of the decay of the coefficients of the polynomial chaos expansion of the solution. Secondly, we consider regression approaches where the PDE is evaluated on randomly chosen points in the probability space and a polynomial approximation constructed by the least square method. We present recent theoretical results on the stability and optimality of the approximation under suitable conditions between the number of sampling points and the dimension of the polynomial space. In particular, we show that for uniform random variables, the number of sampling point has to scale quadratically with the dimension of the polynomial space to maintain the stability and optimality of the approximation. Numerical results show that such condition is sharp in the monovariate case but seems to be over-constraining in higher dimensions. The regression technique seems therefore to be attractive in higher dimensions.

Numerical Methods for Bayesian Inverse Problems

Ernst, Oliver; Sprungk, Bjorn; Cliffe, K. Andrew; Starkloff, Hans-Jorg (2014-01-06) [Presentation]

We present recent results on Bayesian inversion for a groundwater flow problem with an uncertain conductivity field. In particular, we show how direct and indirect measurements can be used to obtain a stochastic model for the unknown. The main tool here is Bayes’ theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements. Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of radionuclide contaminants, can be obtained by Markov Chain Monte Carlo (MCMC) simulations. Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.

Multivariate Max-Stable Spatial Processes

Genton, Marc G. (2014-01-06) [Presentation]

Analysis of spatial extremes is currently based on univariate processes. Max-stable processes allow the spatial dependence of extremes to be modelled and explicitly quantified, they are therefore widely adopted in applications. For a better understanding of extreme events of real processes, such as environmental phenomena, it may be useful to study several spatial variables simultaneously. To this end, we extend some theoretical results and applications of max-stable processes to the multivariate setting to analyze extreme events of several variables observed across space. In particular, we study the maxima of independent replicates of multivariate processes, both in the Gaussian and Student-t cases. Then, we define a Poisson process construction in the multivariate setting and introduce multivariate versions of the Smith Gaussian extremevalue, the Schlather extremal-Gaussian and extremal-t, and the BrownResnick models. Inferential aspects of those models based on composite likelihoods are developed. We present results of various Monte Carlo simulations and of an application to a dataset of summer daily temperature maxima and minima in Oklahoma, U.S.A., highlighting the utility of working with multivariate models in contrast to the univariate case. Based on joint work with Simone Padoan and Huiyan Sang.

Optimal Experimental Design for Large-Scale Bayesian Inverse Problems

Ghattas, Omar (2014-01-06) [Presentation]

We develop a Bayesian framework for the optimal experimental design of the shock tube experiments which are being carried out at the KAUST Clean Combustion Research Center. The unknown parameters are the pre-exponential parameters and the activation energies in the reaction rate expressions. The control parameters are the initial mixture composition and the temperature. The approach is based on first building a polynomial based surrogate model for the observables relevant to the shock tube experiments. Based on these surrogates, a novel MAP based approach is used to estimate the expected information gain in the proposed experiments, and to select the best experimental set-ups yielding the optimal expected information gains. The validity of the approach is tested using synthetic data generated by sampling the PC surrogate. We finally outline a methodology for validation using actual laboratory experiments, and extending experimental design methodology to the cases where the control parameters are noisy.

On the Predictability of Computer simulations: Advances in Verification and Validation

Prudhomme, Serge (2014-01-06) [Presentation]

We will present recent advances on the topics of Verification and Validation in order to assess the reliability and predictability of computer simulations. The first part of the talk will focus on goal-oriented error estimation for nonlinear boundary-value problems and nonlinear quantities of interest, in which case the error representation consists of two contributions: 1) a first contribution, involving the residual and the solution of the linearized adjoint problem, which quantifies the discretization or modeling error; and 2) a second contribution, combining higher-order terms that describe the linearization error. The linearization error contribution is in general neglected with respect to the discretization or modeling error. However, when nonlinear effects are significant, it is unclear whether ignoring linearization effects may produce poor convergence of the adaptive process. The objective will be to show how both contributions can be estimated and employed in an adaptive scheme that simultaneously controls the two errors in a balanced manner. In the second part of the talk, we will present
novel approach for calibration of model parameters. The proposed inverse problem not only involves the minimization of the misfit between experimental observables and their theoretical estimates, but also an objective function that takes into account some design goals on specific design scenarios. The method can be viewed as a regularization approach of the inverse problem, one, however, that best respects some design goals for which mathematical models are intended. The inverse problem is solved by a Bayesian method to account for uncertainties in the data. We will show that it shares the same structure as the deterministic problem that one would obtain by multi-objective optimization theory. The method is illustrated on an example of heat transfer in a two-dimensional fin. The proposed approach has the main benefit that it increases the confidence in predictive capabilities of mathematical models.

Inverse Problems and Uncertainty Quantification

Litvinenko, Alexander; Matthies, Hermann G. (2014-01-06) [Presentation]

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) modelare strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time- consuming and slowly convergent Monte Carlo sampling. The developed sampling- free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.

Multilevel variance estimators in MLMC and application for random obstacle problems

Chernov, Alexey; Bierig, Claudio (2014-01-06) [Presentation]

The Multilevel Monte Carlo Method (MLMC) is a recently established sampling approach for uncertainty propagation for problems with random parameters. In this talk we present new convergence theorems for the multilevel variance estimators. As a result, we prove that under certain assumptions on the parameters, the variance can be estimated at essentially the same cost as the mean, and consequently as the cost required for solution of one forward problem for a fixed deterministic set of parameters. We comment on fast and stable evaluation of the estimators suitable for parallel large scale computations. The suggested approach is applied to a class of scalar random obstacle problems, a prototype of contact between deformable bodies. In particular, we are interested in rough random obstacles modelling contact between car tires and variable road surfaces. Numerical experiments support and complete the theoretical analysis.

Cooperative HARQ with Poisson Interference and Opportunistic Routing

Kaveh, Mostafa; Rajana, Aomgh (2014-01-06) [Presentation]

This presentation considers reliable transmission of data from a source to a destination, aided cooperatively by wireless relays selected opportunistically and utilizing hybrid forward error correction/detection, and automatic repeat request (Hybrid ARQ, or HARQ). Specifically, we present a performance analysis of the cooperative HARQ protocol in a wireless adhoc multihop network employing spatial ALOHA. We model the nodes in such a network by a homogeneous 2-D Poisson point process. We study the tradeoff between the per-hop rate, spatial density and range of transmissions inherent in the network by optimizing the transport capacity with respect to the network design parameters, HARQ coding rate and medium access probability. We obtain an approximate analytic expression for the expected progress of opportunistic routing and optimize the capacity approximation by convex optimization. By way of numerical results, we show that the network design parameters obtained by optimizing the analytic approximation of transport capacity closely follows that of Monte Carlo based exact transport capacity optimization. As a result of the analysis, we argue that the optimal HARQ coding rate and medium access probability are independent of the node density in the network.

A Continuation MLMC algorithm

Collier, Nathan; Haji Ali, Abdul Lateef; Nobile, Fabio; von Schwerin, Erik; Tempone, Raul (2014-01-06) [Poster]

Hybrid Chernoff Tau-Leap

Moraes, Alvaro; Tempone, Raul; Vilanova, Pedro (2014-01-06) [Poster]

Markovian pure jump processes can model many phenomena, e.g. chemical reactions at molecular level, protein transcription and translation, spread of epidemics diseases in small populations and in wireless communication networks among many others. In this work we present a novel hybrid algorithm for simulating individual trajectories which adaptively switches between the SSA and the Chernoff tauleap methods. This allows us to: (a) control the global exit probability
of any simulated trajectory, (b) obtain accurate and computable estimates for the expected value of any smooth observable of the process with minimal computational work.

The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

By default, clicking on the export buttons will result in a download of the allowed maximum amount of items. For anonymous users the allowed maximum amount is 50 search results.

To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.