Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)http://hdl.handle.net/10754/6247812024-05-23T18:34:42Z2024-05-23T18:34:42Z931A multilevel adaptive reaction-splitting method for SRNsMoraes, AlvaroTempone, RaulVilanova, Pedrohttp://hdl.handle.net/10754/6247882023-10-30T22:37:21Z2016-01-06T00:00:00Zdc.title: A multilevel adaptive reaction-splitting method for SRNs
dc.contributor.author: Moraes, Alvaro; Tempone, Raul; Vilanova, Pedro
dc.description.abstract: In [5], we present a novel multilevel Monte Carlo method for kinetic simulation of stochastic reaction networks (SRNs) specifically designed for systems in which the set of reaction channels can be adaptively partitioned into two subsets characterized by either high or low activity. To estimate expected values of observables of the system, our method bounds the global computational error to be below a prescribed tolerance, TOL, within a given confidence level. This is achieved with a computational complexity of order O(TOL-2). We also present a novel control variate technique which may dramatically reduce the variance of the coarsest level at a negligible computational cost.
2016-01-06T00:00:00ZA new smoothing technique for European basket optionsBayer, ChristianSiebenmorgen, MarkusTempone, Raulhttp://hdl.handle.net/10754/6248342024-03-13T12:17:16Z2016-01-06T00:00:00Zdc.title: A new smoothing technique for European basket options
dc.contributor.author: Bayer, Christian; Siebenmorgen, Markus; Tempone, Raul
2016-01-06T00:00:00ZA non-intrusive approach for PC analysis of SDEs driven by Wiener noiseNavarro, MaríaLe Maitre, OlivierKnio, Omarhttp://hdl.handle.net/10754/6248062024-03-13T12:17:24Z2016-01-06T00:00:00Zdc.title: A non-intrusive approach for PC analysis of SDEs driven by Wiener noise
dc.contributor.author: Navarro, María; Le Maitre, Olivier; Knio, Omar
2016-01-06T00:00:00ZA Nonlinear Sparse Electromagnetic Imaging Scheme Accelerated with Projected Steepest Descent AlgorithmDesmal, AbdullaBagci, Hakanhttp://hdl.handle.net/10754/6248202023-10-30T22:37:52Z2016-01-06T00:00:00Zdc.title: A Nonlinear Sparse Electromagnetic Imaging Scheme Accelerated with Projected Steepest Descent Algorithm
dc.contributor.author: Desmal, Abdulla; Bagci, Hakan
2016-01-06T00:00:00ZA potpourri of results from the KAUST SRI-UQTempone, Raulhttp://hdl.handle.net/10754/6248632023-11-30T01:27:29Z2016-01-08T00:00:00Zdc.title: A potpourri of results from the KAUST SRI-UQ
dc.contributor.author: Tempone, Raul
dc.description.abstract: As the KAUST Strategic Research Initiative for Uncertainty Quantification completes its fourth year of existence we recall several results produced during its exciting journey of discovery. These include, among others, contributions on Multi-level and Multi-index sampling techniques that address both direct and inverse problems. We may discuss also several techniques for Bayesian Inverse Problems and Optimal Experimental Design.
2016-01-08T00:00:00ZA Sparsity-Regularized Reconstruction of Two-Dimensional Piecewise Continuous Domains!Sandhu, Ali ImranDesmal, AbdullaBagci, Hakanhttp://hdl.handle.net/10754/6248212024-03-13T12:29:30Z2016-01-06T00:00:00Zdc.title: A Sparsity-Regularized Reconstruction of Two-Dimensional Piecewise Continuous Domains!
dc.contributor.author: Sandhu, Ali Imran; Desmal, Abdulla; Bagci, Hakan
2016-01-06T00:00:00ZA Stochastic Multiscale Method for the Elastic Wave Equations Arising from Fiber CompositesBabuska, IvoMotamed, MohammadTempone, Raulhttp://hdl.handle.net/10754/6248362024-03-13T12:17:14Z2016-01-06T00:00:00Zdc.title: A Stochastic Multiscale Method for the Elastic Wave Equations Arising from Fiber Composites
dc.contributor.author: Babuska, Ivo; Motamed, Mohammad; Tempone, Raul
dc.description.abstract: We present a stochastic multilevel global-local algorithm [1] for computing elastic waves propagating in fiber-reinforced polymer composites, where the material properties and the size and distribution of fibers in the polymer matrix may be random. The method aims at approximating statistical moments of some given quantities of interest, such as stresses, in regions of relatively small size, e.g. hot spots or zones that are deemed vulnerable to failure. For a fiber-reinforced cross-plied laminate, we introduce three problems: 1) macro; 2) meso; and 3) micro problems, corresponding to the three natural length scales: 1) the sizes of plate; 2) the tickles of plies; and 3) and the diameter of fibers. The algorithm uses a homogenized global solution to construct a local approximation that captures the microscale features of the problem. We perform numerical experiments to show the applicability and efficiency of the method.
2016-01-06T00:00:00ZA study of Monte Carlo methods for weak approximations of stochastic particle systems in the mean-field?Haji Ali, Abdul Lateefhttp://hdl.handle.net/10754/6248652023-11-30T01:27:11Z2016-01-08T00:00:00Zdc.title: A study of Monte Carlo methods for weak approximations of stochastic particle systems in the mean-field?
dc.contributor.author: Haji Ali, Abdul Lateef
dc.description.abstract: I discuss using single level and multilevel Monte Carlo methods to compute quantities of interests of a stochastic particle system in the mean-field. In this context, the stochastic particles follow a coupled system of Ito stochastic differential equations (SDEs). Moreover, this stochastic particle system converges to a stochastic mean-field limit as the number of particles tends to infinity. I start by recalling the results of applying different versions of Multilevel Monte Carlo (MLMC) for particle systems, both with respect to time steps and the number of particles and using a partitioning estimator. Next, I expand on these results by proposing the use of our recent Multi-index Monte Carlo method to obtain improved convergence rates.
2016-01-08T00:00:00ZA Unified Simulation Approach for the Fast Outage Capacity Evaluation over Generalized Fading ChannelsRached, Nadhir B.Kammoun, AblaAlouini, Mohamed-SlimTempone, Raulhttp://hdl.handle.net/10754/6248132024-03-13T12:29:31Z2016-01-06T00:00:00Zdc.title: A Unified Simulation Approach for the Fast Outage Capacity Evaluation over Generalized Fading Channels
dc.contributor.author: Rached, Nadhir B.; Kammoun, Abla; Alouini, Mohamed-Slim; Tempone, Raul
dc.description.abstract: The outage capacity (OC) is among the most important performance metrics of communication systems over fading channels. The evaluation of the OC, when equal gain combining (EGC) or maximum ratio combining (MRC) diversity techniques are employed, boils down to computing the cumulative distribution function (CDF) of the sum of channel envelopes (equivalently amplitudes) for EGC or channel gains (equivalently squared enveloped/ amplitudes) for MRC. Closed-form expressions of the CDF of the sum of many generalized fading variates are generally unknown and constitute open problems. We develop a unified hazard rate twisting Importance Sampling (IS) based approach to efficiently estimate the CDF of the sum of independent arbitrary variates. The proposed IS estimator is shown to achieve an asymptotic optimality criterion, which clearly guarantees its efficiency. Some selected simulation results are also shown to illustrate the substantial computational gain achieved by the proposed IS scheme over crude Monte Carlo simulations.
2016-01-06T00:00:00ZAdaptive stochastic Galerkin FEM with hierarchical tensor representationsEigel, Martinhttp://hdl.handle.net/10754/6248622023-11-30T01:27:05Z2016-01-08T00:00:00Zdc.title: Adaptive stochastic Galerkin FEM with hierarchical tensor representations
dc.contributor.author: Eigel, Martin
dc.description.abstract: PDE with stochastic data usually lead to very high-dimensional algebraic problems which easily become unfeasible for numerical computations because of the dense coupling structure of the discretised stochastic operator. Recently, an adaptive stochastic Galerkin FEM based on a residual a posteriori error estimator was presented and the convergence of the adaptive algorithm was shown. While this approach leads to a drastic reduction of the complexity of the problem due to the iterative discovery of the sparsity of the solution, the problem size and structure is still rather limited. To allow for larger and more general problems, we exploit the tensor structure of the parametric problem by representing operator and solution iterates in the tensor train (TT) format. The (successive) compression carried out with these representations can be seen as a generalisation of some other model reduction techniques, e.g. the reduced basis method. We show that this approach facilitates the efficient computation of different error indicators related to the computational mesh, the active polynomial chaos index set, and the TT rank. In particular, the curse of dimension is avoided.
2016-01-08T00:00:00Z