Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)http://hdl.handle.net/10754/6239612021-01-18T18:14:47Z2021-01-18T18:14:47ZSolution of Stochastic Nonlinear PDEs Using Automated Wiener-Hermite ExpansionAl-Juhani, AmnahEl-Beltagy, Mohamedhttp://hdl.handle.net/10754/6239892019-07-31T11:31:10Z2014-01-06T00:00:00ZSolution of Stochastic Nonlinear PDEs Using Automated Wiener-Hermite Expansion
Al-Juhani, Amnah; El-Beltagy, Mohamed
The solution of the stochastic differential equations (SDEs) using Wiener-Hermite 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 Wiener-Hermite 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].
2014-01-06T00:00:00ZDynamical low rank approximation of time dependent PDEs with random dataMusharbashy, EleonoraNobile, FabioZhou, Taohttp://hdl.handle.net/10754/6239922019-03-21T21:28:08Z2014-01-06T00:00:00ZDynamical low rank approximation of time dependent PDEs with random data
Musharbashy, Eleonora; Nobile, Fabio; Zhou, Tao
2014-01-06T00:00:00ZOptimal Experimental Design for Large-Scale Bayesian Inverse ProblemsGhattas, Omarhttp://hdl.handle.net/10754/6240242019-03-21T21:29:42Z2014-01-06T00:00:00ZOptimal Experimental Design for Large-Scale Bayesian Inverse Problems
Ghattas, Omar
We develop a Bayesian framework for the optimal experimental design of the shock tube experiments which are being carried out at the KAUST Clean Combustion Research Center. The unknown parameters are the pre-exponential parameters and the activation energies in the reaction rate expressions. The control parameters are the initial mixture composition and the temperature. The approach is based on first building a polynomial based surrogate model for the observables relevant to the shock tube experiments. Based on these surrogates, a novel MAP based approach is used to estimate the expected information gain in the proposed experiments, and to select the best experimental set-ups yielding the optimal expected information gains. The validity of the approach is tested using synthetic data generated by sampling the PC surrogate. We finally outline a methodology for validation using actual laboratory experiments, and extending experimental design methodology to the cases where the control parameters are noisy.
2014-01-06T00:00:00ZMultilevel variance estimators in MLMC and application for random obstacle problemsChernov, AlexeyBierig, Claudiohttp://hdl.handle.net/10754/6240212019-03-21T21:29:34Z2014-01-06T00:00:00ZMultilevel variance estimators in MLMC and application for random obstacle problems
Chernov, Alexey; Bierig, Claudio
The Multilevel Monte Carlo Method (MLMC) is a recently established sampling approach for uncertainty propagation for problems with random parameters. In this talk we present new convergence theorems for the multilevel variance estimators. As a result, we prove that under certain assumptions on the parameters, the variance can be estimated at essentially the same cost as the mean, and consequently as the cost required for solution of one forward problem for a fixed deterministic set of parameters. We comment on fast and stable evaluation of the estimators suitable for parallel large scale computations. The suggested approach is applied to a class of scalar random obstacle problems, a prototype of contact between deformable bodies. In particular, we are interested in rough random obstacles modelling contact between car tires and variable road surfaces. Numerical experiments support and complete the theoretical analysis.
2014-01-06T00:00:00Z