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

Flow, transport and diffusion in random geometries I: a MLMC algorithm(20150107) [Poster]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 propose a generalpurpose algorithm and computational code for the solution of Partial Differential Equations (PDEs) on random geoemtry and with random parameters. We make use of the key idea of MLMC, based on different discretization levels, extending it in a more general context, making use of a hierarchy of physical resolution scales, solvers, models and other numerical/geometrical discretization parameters. Modifications of the classical MLMC estimators are proposed to further reduce variance in cases where analytical convergence rates and asymptotic regimes are not available. Spheres, ellipsoids and general convexshaped grains are placed randomly in the domain with different placing/packing algorithms and the effective properties of the heterogeneous medium are computed. These are, for example, effective diffusivities, conductivities, and reaction rates. The implementation of the MonteCarlo estimators, the statistical samples and each single solver is done efficiently in parallel.

Error analysis in Fourier methods for option pricing for exponential Lévy processes(20150107) [Poster]We derive an error bound for utilising the discrete Fourier transform method for solving Partial IntegroDifferential Equations (PIDE) that describe european option prices for exponential Lévy driven asset prices. We give sufficient conditions for the existence of a L? bound that separates the dynamical contribution from that arising from the type of the option n in question. The bound achieved does not rely on information of the asymptotic behaviour of option prices at extreme asset values. In addition, we demonstrate improved numerical performance for select examples of practical relevance when compared to established bounding methods.

Hybrid Chernoff TauLeap(20150107) [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.

Multilevel Hybrid Chernoff TauLeap(20150107) [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 [6] we present a novel multilevel algorithm for the Chernoffbased hybrid tauleap algorithm. This variance reduction technique 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.

MultiIndex Monte Carlo (MIMC)(20150107) [Poster]We propose and analyze a novel MultiIndex Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC method is both a stochastic version of the combination technique introduced by Zenger, Griebel and collaborators and an extension of the Multilevel Monte Carlo (MLMC) method first described by Heinrich and Giles. Inspired by Giles’s seminal work, instead of using firstorder differences as in MLMC, we use in MIMC highorder mixed differences to reduce the variance of the hierarchical differences dramatically. Under standard assumptions on the convergence rates of the weak error, variance and work per sample, the optimal index set turns out to be of Total Degree (TD) type. When using such sets, MIMC yields new and improved complexity results, which are natural generalizations of Giles’s MLMC analysis, and which increase the domain of problem parameters for which we achieve the optimal convergence.

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations(20150107) [Poster]Using WienerHermite expansion (WHE) 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]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the GrunwaldLetnikov approximation in case of fractional order and with Coimbra approximation in case of variableorder damping. The numerical solver was tested with the analytic solution and with MonteCarlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

Computable error estimates for FEMs for elliptic PDE with lognormal data(20150107) [Poster]

EnergyAware AmplifyandForwards Relaying Systems with Imperfect Channel Estimation(20150107) [Poster]

The ForwardReverse Algorithm for Stochastic Reaction Networks(20150107) [Poster]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.

Performance Limits of Energy Harvesting Communications under Imperfect Channel State Information(20150107) [Poster]In energy harvesting communications, the transmitters have to adapt transmission to availability of energy harvested during the course of communication. The performance of the transmission depends on the channel conditions which vary randomly due to mobility and environmental changes. In this work, we consider the problem of power allocation taking into account the energy arrivals over time and the degree of channel state information (CSI) available at the transmitter, in order to maximize the throughput. In this work, the CSI at the transmitter is not perfect and may include estimation errors. We solve this problem with respect to the causality and energy storage constraints. We determine the optimal offline policy in the case where the channel is assumed to be perfectly known at the receiver. Different cases of CSI availability are studied for the transmitter. We obtain the power policy when the transmitter has either perfect CSI or no CSI. We also investigate of utmost interest the case of fading channels with imperfect CSI. Furthermore, we analyze the asymptotic average throughput in a system where the average recharge rate goes asymptotically to zero and when it is very high.

Fullydistributed randomized cooperation in wireless sensor networks(20150107) [Poster]When marrying randomized distributed spacetime coding (RDSTC) to geographical routing, new performance horizons can be created. In order to reach those horizons however, routing protocols must evolve to operate in a fully distributed fashion. In this letter, we expose a technique to construct a fully distributed geographical routing scheme in conjunction with RDSTC. We then demonstrate the performance gains of this novel scheme by comparing it to one of the prominent classical schemes.

Power Efficient Low Complexity Precoding for Massive MIMO Systems(20150107) [Poster]

A Novel Time Domain Method for Characterizing Plasmonic Field Interactions(20150107) [Poster]

Sparse Electromagnetic Imaging Using Nonlinear Landweber Iterations(20150107) [Poster]

Multiphase flows in complex geometries: a UQ perspective(20150107) [Presentation]Nowadays computer simulations are widely used in many multiphase flow applications involving interphases, dispersed particles, and complex geometries. Most of these problems are solved with mixed models composed of fundamental physical laws, rigorous mathematical upscaling, and empirical correlations/closures. This means that classical inference techniques or forward parametric studies, for example, becomes computationally prohibitive and must take into account the physical meaning and constraints of the equations. However mathematical techniques commonly used in Uncertainty Quantification can come to the aid for the (i) modeling, (ii) simulation, and (iii) validation steps. Two relevant applications for environmental, petroleum, and chemical engineering will be presented to highlight these aspects and the importance of bridging the gaps between engineering applications, computational physics and mathematical methods. The first example is related to the mathematical modeling of subgrid/subscale information with Probability Density Function (PDF) models in problems involving flow, mixing, and reaction in random environment. After a short overview of the research field, some connections and similarities with Polynomial Chaos techniques, will be investigated. In the second example, averaged correlations laws and effective parameters for multiphase flow and their statistical fluctuations, will be considered and efficient computational techniques, borrowed from highdimensional stochastic PDE problems, will be applied. In presence of interfacial flow, where small spatial scales and fast time scales are neglected, the assessment of robustness and predictive capabilities are studied. These illustrative examples are inspired by common problems arising, for example, from the modeling and simulation of turbulent and porous media flows.

Surrogate models and optimal design of experiments for chemical kinetics applications(20150107) [Presentation]Kinetic models for reactive flow applications comprise hundreds of reactions describing the complex interaction among many chemical species. The detailed knowledge of the reaction parameters is a key component of the design cycle of nextgeneration combustion devices, which aim at improving conversion efficiency and reducing pollutant emissions. Shock tubes are a laboratory scale experimental configuration, which is widely used for the study of reaction rate parameters. Important uncertainties exist in the values of the thousands of parameters included in the most advanced kinetic models. This talk discusses the application of uncertainty quantification (UQ) methods to the analysis of shock tube data as well as the design of shock tube experiments. Attention is focused on a spectral framework in which uncertain inputs are parameterized in terms of canonical random variables, and quantities of interest (QoIs) are expressed in terms of a meansquare convergent series of orthogonal polynomials acting on these variables. We outline the implementation of a recent spectral collocation approach for determining the unknown coefficients of the expansion, namely using a sparse, adaptive pseudospectral construction that enables us to obtain surrogates for the QoIs accurately and efficiently. We first discuss the utility of the resulting expressions in quantifying the sensitivity of QoIs to uncertain inputs, and in the Bayesian inference key physical parameters from experimental measurements. We then discuss the application of these techniques to the analysis of shocktube data and the optimal design of shocktube experiments for two key reactions in combustion kinetics: the chainbrancing reaction H + O2 ←→ OH + O and the reaction of Furans with the hydroxyl radical OH.

Robust Optimization of the Self scheduling and Market Involvement for an Electricity Producer(20150107) [Presentation]This work address the optimization under uncertainty of the selfscheduling, forward contracting, and pool involvement of an electricity producer operating a mixed power generation station, which combines thermal, hydro and wind sources, and uses a twostage adaptive robust optimization approach. In this problem the wind power production and the electricity pool price are considered to be uncertain, and are described by uncertainty convex sets. Two variants of a constraint generation algorithm are proposed, namely a primal and dual version, and they are used to solve two case studies based on two different producers. Their market strategies are investigated for three different scenarios, corresponding to as many instances of electricity price forecasts. The effect of the producers’ approach, whether conservative or more risk prone, is also investigated by solving each instance for multiple values of the socalled budget parameter. It was possible to conclude that this parameter influences markedly the producers’ strategy, in terms of scheduling, profit, forward contracting, and pool involvement. Regarding the computational results, these show that for some instances, the two variants of the algorithms have a similar performance, while for a particular subset of them one variant has a clear superiority