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Tempone, Raul (81)

Nobile, Fabio (15)Moraes, Alvaro (14)Vilanova, Pedro (14)Litvinenko, Alexander (8)View MoreDepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (79)Applied Mathematics and Computational Science Program (75)Physical Sciences and Engineering (PSE) Division (7)Electrical Engineering Program (4)Mechanical Engineering Program (4)View MoreSubjectSampling (18)Bayesian (10)Applications (5)Low-Rank (2)approximate covariance (1)View MoreTypePoster (81)Year (Issue Date)2019 (1)2018 (2)2017 (1)2016 (28)2015 (27)View MoreItem AvailabilityOpen Access (81)

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Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method

Litvinenko, Alexander; Yucel, Abdulkadir; Bagci, Hakan; Oppelstrup, Jesper; Tempone, Raul; Michielssen, Eric (2019-02-14) [Poster]

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.

A Case Study of Seismic Wave Propagation with Random Parameters

Ballesio, Marco; Beck, Joakim; Pandey, Anamika; Parisi, Laura; von Schwerin, Erik; Tempone, Raul (2018-09-07) [Poster]

We will present results from a case study based on an earthquake with seismograms recorded on a small dense seismic network in the Ngorongoro Conservation Area in Tanzania. We consider forward seismic wave propagation in an inhomogeneous linear viscoelastic media with random wave speeds and densities, subject to deterministic boundary and initial conditions. The random parameters model the inherent uncertainty of the Earth parameters. We use multilevel Monte Carlo simulations for computing statistics of quantities of interest chosen to formulate a suitable loss function for the corresponding source inversion problem.
We use recorded seismograms to study a noise model for use in Bayesian inverse problems. This work provides a benchmark for the implementation of Multilevel algorithms to accelerate Seismic Inversion addressing earthquake source estimation as well as inferring Earth structure.

Multilevel Monte Carlo (MLMC) Acceleration of Seismic Wave Propagation under Uncertainty

Ballesio, Marco; Beck, Joakim; Pandey, Anamika; Parisi, Laura; von Schwerin, Erik; Tempone, Raul (2018-04-13) [Poster]

We consider forward seismic wave propagation in an inhomogeneous linear viscoelastic media with random wave speed subjected to deterministic boundary and initial conditions. Considering random wave speed correspond to the inclusion of inherent uncertainty of the Earth parameters. We propose multilevel Monte Carlo simulation for computing statistics of some given quantities of interest. In this poster, we will present a case study from Tanzania to quantify uncertainty in Earth's parameters. This work provides a benchmark for the implementation of Multilevel algorithms to accelerate Seismic Inversion addressing earthquake source estimation as well as inferring Earth structure.

Risk assessment of salt contamination of groundwater under uncertain aquifer properties

Litvinenko, Alexander; Keyes, David E.; Logashenko, Dmitry; Tempone, Raul; Wittum, Gabriel (2017-10-01) [Poster]

One of the central topics in hydrogeology and environmental science is the investigation of salinity-driven groundwater flow in heterogeneous porous media. Our goals are to model and to predict pollution of water resources.
We simulate a density driven groundwater flow with uncertain porosity and permeability. This strongly non-linear model describes the unstable transport of salt water with building ‘fingers’-shaped patterns. The computation requires
a very fine unstructured mesh and, therefore, high computational resources.
We run the highly-parallel multigrid solver, based on ug4, on supercomputer Shaheen II. A MPI-based parallelization is done in the geometrical as well as in the stochastic spaces. Every scenario is computed on 32 cores and
requires a mesh with ~8M grid points and 1500 or more time steps. 200 scenarios are computed concurrently. The total number of cores in parallel computation is 200x32=6400. The main goal of this work is to estimate propagation of uncertainties through the model, to investigate sensitivity of the solution to the input uncertain parameters. Additionally, we demonstrate how the multigrid ug4-based solver can be applied as a black-box in the uncertainty quantification framework.

Fast Fourier Transform Pricing Method for Exponential Lévy Processes

Flores, Fabian Crocce; Häppölä, Juho; Kiessling, Jonas; Tempone, Raul (2014-05-04) [Poster]

We describe a set of partial-integro-differential equations (PIDE) whose solutions represent the prices of european options when the underlying asset is driven by an exponential L´evy process. Exploiting the L´evy -Khintchine formula, we give a Fourier based method for solving this class of PIDEs. We present a novel L1 error bound for solving a range of PIDEs in asset pricing and use this bound to set parameters for numerical methods.

Quasi-optimal sparse-grid approximations for elliptic PDEs with stochastic coefficients

Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul (2014-05-04) [Poster]

Computation of High-Frequency Waves with Random Uncertainty

Malenova, Gabriela; Motamed, Mohammad; Runborg, Olof; Tempone, Raul (2016-01-06) [Poster]

We consider the forward propagation of uncertainty in high-frequency waves, described by the second order wave equation with highly oscillatory initial data. The main sources of uncertainty are the wave speed and/or the initial phase and amplitude, described by a finite number of random variables with known joint probability distribution. We propose a stochastic spectral asymptotic method [1] for computing the statistics of uncertain output quantities of interest (QoIs), which are often linear or nonlinear functionals of the wave solution and its spatial/temporal derivatives. The numerical scheme combines two techniques: a high-frequency method based on Gaussian beams [2, 3], a sparse stochastic collocation method [4]. The fast spectral convergence of the proposed method depends crucially on the presence of high stochastic regularity of the QoI independent of the wave frequency. In general, the high-frequency wave solutions to parametric hyperbolic equations are highly oscillatory and non-smooth in both physical and stochastic spaces. Consequently, the stochastic regularity of the QoI, which is a functional of the wave solution, may in principle below and depend on frequency. In the present work, we provide theoretical arguments and numerical evidence that physically motivated QoIs based on local averages of |uE|2 are smooth, with derivatives in the stochastic space uniformly bounded in E, where uE and E denote the highly oscillatory wave solution and the short wavelength, respectively. This observable related regularity makes the proposed approach more efficient than current asymptotic approaches based on Monte Carlo sampling techniques.

A Stochastic Multiscale Method for the Elastic Wave Equations Arising from Fiber Composites

Babuska, Ivo; Motamed, Mohammad; Tempone, Raul (2016-01-06) [Poster]

We present a stochastic multilevel global-local algorithm [1] for computing elastic waves propagating in fiber-reinforced polymer composites, where the material properties and the size and distribution of fibers in the polymer matrix may be random. The method aims at approximating statistical moments of some given quantities of interest, such as stresses, in regions of relatively small size, e.g. hot spots or zones that are deemed vulnerable to failure. For a fiber-reinforced cross-plied laminate, we introduce three problems: 1) macro; 2) meso; and 3) micro problems, corresponding to the three natural length scales: 1) the sizes of plate; 2) the tickles of plies; and 3) and the diameter of fibers. The algorithm uses a homogenized global solution to construct a local approximation that captures the microscale features of the problem. We perform numerical experiments to show the applicability and efficiency of the method.

Flow in Random Microstructures: a Multilevel Monte Carlo Approach

Icardi, Matteo; Tempone, Raul (2016-01-06) [Poster]

In this work we are interested in the fast estimation of effective parameters of random heterogeneous materials using Multilevel Monte Carlo (MLMC). MLMC is an efficient and flexible solution for the propagation of uncertainties in complex models, where an explicit parametrisation of the input randomness is not available or too expensive. We propose a general-purpose algorithm and computational code for the solution of Partial Differential Equations (PDEs) on random heterogeneous materials. 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 discretisation 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 convex-shaped 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 Monte-Carlo estimators, the statistical samples and each single solver is done efficiently in parallel. The method is tested and applied for pore-scale simulations of random sphere packings.

Optimal design of experiments considering noisy control parameters
for the inference of Furan combustion reaction rate

Long, Quan; Kim, Daesang; Bisetti, Fabrizio; Farooq, Aamir; Tempone, Raul; Knio, Omar (2016-01-06) [Poster]

We carry out the design of experiments for the identification of the reaction
parameters in Furan combustion. The lacks of information on the true value
of the control parameters, specifically, the initial temperature and the initial TBHP concentration, are considered in the design procedure by errors-invariables models. We use two types of observables. The first is a scaler observable, i.e., half decay time of the [TBHP]. The second is the time history of the concentration.

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