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AuthorTempone, Raul (27)Alouini, Mohamed-Slim (10)Litvinenko, Alexander (9)Bagci, Hakan (8)Ulku, Huseyin Arda (6)View MoreDepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (49)Applied Mathematics and Computational Science Program (28)Electrical Engineering Program (17)Physical Sciences and Engineering (PSE) Division (5)Mechanical Engineering Program (3)View MoreSubjecthierarchical matrices (3)approximate covariance (1)Chlorophyll-Specific Absorption Coefficient (1)data compression (1)Decomposition (1)View MoreTypePoster (55)Year (Issue Date)

2015 (55)

Item AvailabilityOpen Access (55)

Now showing items 31-40 of 55

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Sparse Electromagnetic Imaging Using Nonlinear Landweber Iterations

Desmal, Abdulla; Bagci, Hakan (2015-01-07) [Poster]

Bayesian Optimal Experimental Design Using Multilevel Monte Carlo

Ben Issaid, Chaouki; Long, Quan; Scavino, Marco; Tempone, Raul (2015-01-07) [Poster]

Experimental design is very important since experiments are often resource-exhaustive and time-consuming. We carry out experimental design in the Bayesian framework. To measure the amount of information, which can be extracted from the data in an experiment, we use the expected information gain as the utility function, which specifically is the expected logarithmic ratio between the posterior and prior distributions. Optimizing this utility function enables us to design experiments that yield the most informative data for our purpose. One of the major difficulties in evaluating the expected information gain is that the integral is nested and can be high dimensional. We propose using Multilevel Monte Carlo techniques to accelerate the computation of the nested high dimensional integral. The advantages are twofold. First, the Multilevel Monte Carlo can significantly reduce the cost of the nested integral for a given tolerance, by using an optimal sample distribution among different sample averages of the inner integrals. Second, the Multilevel Monte Carlo method imposes less assumptions, such as the concentration of measures, required by Laplace method. We test our Multilevel Monte Carlo technique using a numerical example on the design of sensor deployment for a Darcy flow problem governed by one dimensional Laplace equation. We also compare the performance of the Multilevel Monte Carlo, Laplace approximation and direct double loop Monte Carlo.

Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

Ruggeri, Fabrizio; Sawlan, Zaid A; Scavino, Marco; Tempone, Raul (2015-01-07) [Poster]

In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.

Dimension-Independent Likelihood-Informed MCMC

Cui, Tiangang; Law, Kody; Marzouk, Youssef (2015-01-07) [Poster]

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters, which in principle can be described as functions. By exploiting low-dimensional structure in the change from prior to posterior [distributions], we introduce a suite of MCMC samplers that can adapt to the complex structure of the posterior distribution, yet are well-defined on function space. Posterior sampling in nonlinear inverse problems arising from various partial di erential equations and also a stochastic differential equation are used to demonstrate the e ciency of these dimension-independent likelihood-informed samplers.

Minimum mean square error estimation and approximation of the Bayesian update

Litvinenko, Alexander; Matthies, Hermann G.; Zander, Elmar (2015-01-07) [Poster]

Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(w), a measurement operator Y (u(q); q), where u(q; w) uncertain solution. Aim: to identify q(w). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(w) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a functional approximation, e.g. polynomial chaos expansion (PCE). New: We derive linear, quadratic etc approximation of full Bayesian update.

Mean-field Ensemble Kalman Filter

Law, Kody; Tembine, Hamidou; Tempone, Raul (2015-01-07) [Poster]

A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d < 2 . The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.

On the Symbol Error Rate of M-ary MPSK over Generalized Fading Channels with Additive Laplacian Noise

Soury, Hamza; Alouini, Mohamed-Slim (2015-01-07) [Poster]

This work considers the symbol error rate of M-ary phase shift keying (MPSK) constellations over extended Generalized-K fading with Laplacian noise and using a minimum distance detector. A generic closed form expression of the conditional and the average probability of error is obtained and simplified in terms of the Fox’s H function. More simplifications to well known functions for some special cases of fading are also presented. Finally, the mathematical formalism is validated with some numerical results examples done by computer based simulations [1].

A Game Theoretical Approach for Cooperative Environmentally Friendly Cellular Networks Powered by the Smart Grid

Ghazzai, Hakim; Yaacoub, Elias; Alouini, Mohamed-Slim (2015-01-07) [Poster]

Energy-Efficient Power Allocation of Cognitive Radio Systems without CSI at the Transmitter

Sboui, Lokman; Rezki, Zouheir; Alouini, Mohamed-Slim (2015-01-07) [Poster]

Two major issues are facing today’s wireless communications evolution: -Spectrum scarcity: Need for more bandwidth. As a solution, the Cognitive Radio (CR) paradigm, where secondary users (unlicensed) share the spectrum with licensed users, was introduced. -Energy consumption and CO2 emission: The ICT produce 2% of global CO2 emission (equivalent to the aviation industry emission). The cellular networks produces 0.2%. As solution energy efficient systems should be designed rather than traditional spectral efficient systems. In this work, we aim to determine the optimal energy efficient power allocation of CR when the channel state information at the transmitter CSI-T is not available.

Time-Lapse Seismic Data assisted History Matching of the Norne Field

Katterbauer, Klemens (2015-01-07) [Poster]

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