Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)
Recent Submissions

The Red Sea Forecasting System(20140106) [Poster]

Multiscale Modeling of Wear Degradation(20140106) [Poster]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.

Time dependent meanfield games(20140106) [Poster]We consider time dependent meanfield games (MFG) with a local powerlike dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension. In the subquadratic case this is done by combining a GagliardoNirenberg type of argument with a new class of polynomial estimates for solutions of the FokkerPlanck equation in terms of LrLp norms of DpH. These techniques do not apply to the superquadratic case. In this setting we recur to a delicate argument that combines the nonlinear adjoint method with polynomial estimates for solutions of the FokkerPlanck equation in terms of L1L1norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of HamiltonJacobi equations with superquadratic Hamiltonians.

Mean Field Game for Marriage(20140106) [Poster]The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an alltime high. This work describes a unique paradigm for preserving relationships and marital stability from meanfield game theory. We show that optimizing the longterm wellbeing via effort and society feeling state distribution will help in stabilizing relationships.

Nonlinear Bayesian update of PCE coefficients(20140106) [Poster]Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally illposed. To identify q(!) we derived nonlinear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).

A Bayesian setting for an inverse problem in heat transfer(20140106) [Poster]In this work a Bayesian setting is developed to infer the thermal conductivity, an unknown parameter that appears into heat equation. Temperature data are available on the basis of cooling experiments. The realistic assumption that the boundary data are noisy is introduced, for a given prescribed initial condition. We show how to derive the global likelihood function for the forward boundaryinitial condition problem, given the values of the temperature field plus Gaussian noise. We assume that the thermal conductivity parameter can be modelled a priori through a lognormal distributed random variable or by means of a spacedependent stationary lognormal random field. In both cases, given Gaussian priors for the timedependent Dirichlet boundary values, we marginalize out analytically the joint posterior distribution of and the random boundary conditions, TL and TR, using the linearity of the heat equation. Synthetic data are used to carry out the inference. We exploit the concentration of the posterior distribution of , using the Laplace approximation and therefore avoiding costly MCMC computations.

A Continuation MLMC algorithm(20140106) [Poster]

Fast Estimation of Expected Information Gain for Bayesian Experimental Design Based on Laplace Approximation(20140106) [Poster]Shannontype expected information gain is an important utility in evaluating the usefulness of a proposed experiment that involves uncertainty. Its estimation, however, cannot rely solely on Monte Carlo sampling methods, that are generally too computationally expensive for realistic physical models, especially for those involving the solution of stochastic partial differential equations. In this work we present a new methodology, based on the Laplace approximation of the posterior probability density function, to accelerate the estimation of expected information gain in the model parameters and predictive quantities of interest. Furthermore, in order to deal with the issue of dimensionality in a complex problem, we use sparse quadratures for the integration over the prior. We show the accuracy and efficiency of the proposed method via several nonlinear numerical examples, including a single parameter design of one dimensional cubic polynomial function and the current pattern for impedance tomography.

Hybrid Chernoff TauLeap(20140106) [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.

Multi Level Monte Carlo methods with Control Variate for elliptic SPDEs(20140106) [Poster]

Dynamical low rank approximation of time dependent PDEs with random data(20140106) [Poster]

Quasioptimal sparsegrid approximations for elliptic PDEs with stochastic coefficients(20140106) [Poster]

Simulation of soot size distribution in an ethylene counterflow flame(20140106) [Poster]Soot, an aggregate of carbonaceous particles produced during the rich combustion of fossil fuels, is an undesirable pollutant and health hazard. Soot evolution involves various dynamic processes: nucleation soot formation from polycyclic aromatic hydrocarbons (PAHs) condensation PAHs condensing on soot particle surface surface processes hydrogenabstractionC2H2addition, oxidation coagulation two soot particles coagulating to form a bigger particle This simulation work investigates soot size distribution and morphology in an ethylene counterflow flame, using i). Chemkin with a method of moments to deal with the coupling between vapor consumption and soot formation; ii). Monte Carlo simulation of soot dynamics.

Multivariate polynomial approximation by means of random discrete least squares(20140106) [Poster]

Kriging accelerated by orders of magnitude: combining lowrank with FFT techniques(20140106) [Poster]Kriging algorithms based on FFT, the separability of certain covariance functions and lowrank representations of covariance functions have been investigated. The current study combines these ideas, and so combines the individual speedup factors of all ideas. The reduced computational complexity is O(dLlogL), where L := max ini, i = 1..d. For separable covariance functions, the results are exact, and nonseparable covariance functions can be approximated through sums of separable components. Speedup factor is 10 8, problem sizes 15e + 12 and 2e + 15 estimation points for Kriging and spatial design.

Reduced Rank Adaptive Filtering in Impulsive Noise Environments(20140106) [Poster]An impulsive noise environment is used in this paper. A new aspect of signal truncation is deployed to reduce the harmful effect of the impulsive noise to the signal. A full rank direct solution is derived followed by an iterative solution. The reduced rank adaptive filter is presented in this environment by using two methods for rank reduction. The minimized objective function is defined using the Lp norm. The results are presented and the efficiency of each algorithm is discussed.

Multiscale Bayesian model for uncertainty quantification in porous media(20140106) [Poster]