Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
Recent Submissions

An Efficient Simulation Method for Rare Events(20150107)Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a wellknown challenging problem. Closedform expressions for the sum distribution do not generally exist, which has led to an increasing interest in simulation approaches. A crude Monte Carlo (MC) simulation is the standard technique for the estimation of this type of probability. However, this approach is computationally expensive, especially when dealing with rare events. Variance reduction techniques are alternative approaches that can improve the computational efficiency of naive MC simulations. We propose an Importance Sampling (IS) simulation technique based on the wellknown hazard rate twisting approach, that presents the advantage of being asymptotically optimal for any arbitrary RVs. The wide scope of applicability of the proposed method is mainly due to our particular way of selecting the twisting parameter. It is worth observing that this interesting feature is rarely satisfied by variance reduction algorithms whose performances were only proven under some restrictive assumptions. It comes along with a good efficiency, illustrated by some selected simulation results comparing the performance of our method with that of an algorithm based on a conditional MC technique.

Kuramoto model for infinite graphs with kernels(20150107)In this paper we study the Kuramoto model of weakly coupled oscillators for the case of non trivial network with large number of nodes. We approximate of such configurations by a McKeanVlasov stochastic differential equation based on infinite graph. We focus on circulant graphs which have enough symmetries to make the computations easier. We then focus on the asymptotic regime where an integropartial differential equation is derived. Numerical analysis and convergence proofs of the FokkerPlanckKolmogorov equation are conducted. Finally, we provide numerical examples that illustrate the convergence of our method.

Multiscale Modeling of Wear Degradation(20150107)Cylinder liners of diesel engines used for marine propulsion are naturally subjected to a wear process, and may fail when their wear exceeds a specified limit. Since failures often represent high economical costs, it is utterly important to predict and avoid them. In this work [4], we model the wear process using a pure jump process. Therefore, the inference goal here is to estimate: the number of possible jumps, its sizes, the coefficients and the shapes of the jump intensities. We propose a multiscale approach for the inference problem that can be seen as an indirect inference scheme. We found that using a Gaussian approximation based on moment expansions, it is possible to accurately estimate the jump intensities and the jump amplitudes. We obtained results equivalent to the state of the art but using a simpler and less expensive approach.

Flow, transport and diffusion in random geometries II: applications(20150107)Multilevel Monte Carlo (MLMC) is an efficient and flexible solution for the propagation of uncertainties in complex models, where an explicit parametrization of the input randomness is not available or too expensive. We present several applications of our MLMC algorithm for flow, transport and diffusion in random heterogeneous materials. The absolute permeability and effective diffusivity (or formation factor) of microscale porous media samples are computed and the uncertainty related to the sampling procedures is studied. The algorithm is then extended to the transport problems and multiphase flows for the estimation of dispersion and relative permeability curves. The impact of water drops on random stuctured surfaces, with microfluidics applications to selfcleaning materials, is also studied and simulated. Finally the estimation of new drag correlation laws for polydispersed dilute and dense suspensions is presented.

On the detectability of transverse cracks in laminated composites through measurements of electrical potential change(20150107)For structures made of laminated composites, realtime structural health monitoring is necessary as significant damage may occur without any visible signs on the surface. Inspection by electrical tomography seems a viable approach as the technique relies on voltage measurements from a network of electrodes over the boundary of the inspected domain to infer the change in conductivity within the bulk material. The change in conductivity, if significant, can be correlated to the degradation state of the material, allowing damage detection. We focus here on the detection of the transverse cracking mechanism which modifies the inplane transverse conductivity of ply. The quality of detection is directly related to the sensitivity of the voltage measurements with respect to the presence of cracks. We demonstrate here from numerical experiments that the sensitivity depends on several parameters, such as the anisotropy in the electrical conductivity of the baseline composite ply or the geometricalparameters of the structure. Based on these results, applicability of electrical tomography to detect transverse cracks in a laminate is discussed.

Cooperative Game for Fish Harvesting and Pollution Control(20150107)We study fishery strategies in a shallow river subject to agricultural and industrial pollution. The flowing pollutants in the river are modeled by a nonlinear stochastic differential equation in a general manner. The logistic growth model for the fish population is modified to cover the pollution impact on the fish growth rate. A stochastic cooperative game is formulated to design strategies for preserving the fish population by controlling the pollution as well as the harvesting fish.

A Hybrid DGTDMNA Scheme for Analyzing Complex Electromagnetic Systems(20150107)A hybrid electromagnetics (EM)circuit simulator for analyzing complex systems consisting of EM devices loaded with nonlinear multiport lumped circuits is described. The proposed scheme splits the computational domain into two subsystems: EM and circuit subsystems, where field interactions are modeled using Maxwell and Kirchhoff equations, respectively. Maxwell equations are discretized using a discontinuous Galerkin time domain (DGTD) scheme while Kirchhoff equations are discretized using a modified nodal analysis (MNA)based scheme. The coupling between the EM and circuit subsystems is realized at the lumped ports, where related EM fields and circuit voltages and currents are allowed to “interact’’ via numerical flux. To account for nonlinear lumped circuit elements, the standard NewtonRaphson method is applied at every time step. Additionally, a local timestepping scheme is developed to improve the efficiency of the hybrid solver. Numerical examples consisting of EM systems loaded with single and multiport linear/nonlinear circuit networks are presented to demonstrate the accuracy, efficiency, and applicability of the proposed solver.

The ForwardReverse Algorithm for Stochastic Reaction Networks(20150107)In this work, we present an extension of the forwardreverse algorithm by Bayer and Schoenmakers [2] to the context of stochastic reaction networks (SRNs). We then apply this bridgegeneration technique to the statistical inference problem of approximating the reaction coefficients based on discretely observed data. To this end, we introduce a twophase iterative inference method in which we solve a set of deterministic optimization problems where the SRNs are replaced by the classical ODE rates; then, during the second phase, the Monte Carlo version of the EM algorithm is applied starting from the output of the previous phase. Starting from a set of overdispersed seeds, the output of our twophase method is a cluster of maximum likelihood estimates obtained by using convergence assessment techniques from the theory of Markov chain Monte Carlo.

A multilevel adaptive reactionsplitting method for SRNs(20150107)In this work, we present a novel multilevel Monte Carlo method for kinetic simulation of stochastic reaction networks 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, within a given confidence level. This is achieved with a computational complexity of order O (TOL2).We also present a novel control variate technique which may dramatically reduce the variance of the coarsest level at a negligible computational cost. Our numerical examples show substantial gains with respect to the standard Stochastic Simulation Algorithm (SSA) by Gillespie and also our previous hybrid Chernoff tauleap method.

On the Symbol Error Rate of Mary MPSK over Generalized Fading Channels with Additive Laplacian Noise(20150107)This work considers the symbol error rate of Mary phase shift keying (MPSK) constellations over extended GeneralizedK 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].

Bayesian Optimal Experimental Design Using Multilevel Monte Carlo(20150107)Experimental design is very important since experiments are often resourceexhaustive and timeconsuming. 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.

Minimum mean square error estimation and approximation of the Bayesian update(20150107)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 illposed. To identify q(w) we derived nonlinear 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.

Hierarchical matrix approximation of large covariance matrices(20150107)We approximate large nonstructured covariance matrices in the Hmatrix format with a loglinear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in Hformat. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design