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

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.

The Red Sea Forecasting System(20140106) [Poster]

Two phase simulation and Bayesian inversion for CO2 storage in porous media(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.

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.

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).

DataDriven Model Order Reduction for Bayesian Inverse Problems(20140106) [Poster]One of the major challenges in using MCMC for the solution of inverse problems is the repeated evaluation of computationally expensive numerical models. We develop a datadriven projection based model order reduction technique to reduce the computational cost of numerical PDE evaluations in this context.

A SparseDiscontinuous Galerkin method for the VlasovPoisson System(20140106) [Poster]

Boundary Feedback Control of Shallow Water Flow(20140106) [Poster]We design boundary feedback control laws from the linearized shallow water model to stabilize nonlinear shallow flow around a given state.

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.

Higherorder Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique(20140106) [Poster]Using WienerHermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The WienerHermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic WienerHermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.

Solution of Stochastic Nonlinear PDEs Using Automated WienerHermite Expansion(20140106) [Poster]The solution of the stochastic differential equations (SDEs) using WienerHermite expansion (WHE) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic WienerHermite coefficients. In WHE approach, there is no randomness directly involved in the computations. One does not have to rely on pseudo random number generators, and there is no need to solve the SDEs repeatedly for many realizations. Instead, the deterministic system is solved only once. For previous research efforts see [2, 4].