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AuthorTempone, Raul (25)Moraes, Alvaro (5)Vilanova, Pedro (5)Litvinenko, Alexander (3)Nobile, Fabio (3)View MoreDepartment

Applied Mathematics and Computational Science Program (28)

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (28)Clean Combustion Research Center (2)Electrical Engineering Program (2)Mechanical Engineering Program (2)View MoreTypePoster (28)Year (Issue Date)
2015 (28)

Item AvailabilityOpen Access (28)

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Computation of Electromagnetic Fields Scattered From Dielectric Objects of Uncertain Shapes Using MLMC

Litvinenko, Alexander; Haji Ali, Abdul Lateef; Uysal, Ismail Enes; Ulku, Huseyin Arda; Tempone, Raul; Bagci, Hakan; Oppelstrup, Jesper (2015-01-07) [Poster]

Simulators capable of computing scattered fields from objects of uncertain shapes are highly useful in electromagnetics and photonics, where device designs are typically subject to fabrication tolerances. Knowledge of statistical variations in scattered fields is useful in ensuring error-free functioning of devices. Oftentimes such simulators use a Monte Carlo (MC) scheme to sample the random domain, where the variables parameterize the uncertainties in the geometry. At each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver is executed to compute the scattered fields. However, to obtain accurate statistics of the scattered fields, the number of MC samples has to be large.
This significantly increases the total execution time. In this work, to address this challenge, the Multilevel MC (MLMC [1]) scheme is used together with a (deterministic) surface integral equation solver. The MLMC achieves a higher efficiency by “balancing” the statistical errors due to sampling of the random domain and the numerical errors due to discretization of the geometry at each of these samples. Error balancing results in a smaller number of samples requiring coarser discretizations. Consequently, total execution time is significantly shortened.

Kuramoto model for infinite graphs with kernels

Canale, Eduardo; Tembine, Hamidou; Tempone, Raul; Zouraris, Georgios E. (2015-01-07) [Poster]

In this paper we study the Kuramoto model of weakly coupled oscillators for the case of non trivial network with large number of nodes. We approximate of such configurations by a McKean-Vlasov stochastic differential equation based on infinite graph. We focus on circulant graphs which have enough symmetries to make the computations easier. We then focus on the asymptotic regime where an integro-partial differential equation is derived. Numerical analysis and convergence proofs of the Fokker-Planck-Kolmogorov equation are conducted. Finally, we provide numerical examples that illustrate the convergence of our method.

An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

Karlsson, Peer Jesper; Larsson, Stig; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul (2015-01-07) [Poster]

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading order term consisting of an error density that is computable from Symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations.

Optimal Experimental Design of Furan Shock Tube Kinetic Experiments

Kim, Daesang; Long, Quan; Bisetti, Fabrizio; Farooq, Aamir; Tempone, Raul; Knio, Omar (2015-01-07) [Poster]

A Bayesian optimal experimental design methodology has been developed and applied to refine the rate coefficients of elementary reactions in Furan combustion. Furans are considered as potential renewable fuels. We focus on the Arrhenius rates of Furan + OH ↔ Furyl-2 + H2O and Furan ↔ OH Furyl-3 + H2O, and rely on the OH consumption rate as experimental observable. A polynomial chaos surrogate is first constructed using an adaptive pseudo-spectral projection algorithm. The PC surrogate is then exploited in conjunction with a fast estimation of the expected information gain in order to determine the optimal design in the space of initial temperatures and OH concentrations.

Spectral Uncertainty Analysis of Ionic Reactions in Methane Combustion

Kim, Daesang; Han, Jie; Bisetti, Fabrizio; Farooq, Aamir; Knio, Omar (2015-01-07) [Poster]

Multiscale Modeling of Wear Degradation

Moraes, Alvaro; Ruggeri, Fabrizio; Tempone, Raul; Vilanova, Pedro (2015-01-07) [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.

Flow, transport and diffusion in random geometries II: applications

Asinari, Pietro; Ceglia, Diego; Icardi, Matteo; Prudhomme, Serge; Tempone, Raul (2015-01-07) [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 present several applications of our MLMC algorithm for flow, transport and diffusion in random heterogeneous materials. The absolute permeability and effective diffusivity (or formation factor) of micro-scale porous media samples are computed and the uncertainty related to the sampling procedures is studied. The algorithm is then extended to the transport problems and multiphase flows for the estimation of dispersion and relative permeability curves. The impact of water drops on random stuctured surfaces, with microfluidics applications to self-cleaning materials, is also studied and simulated. Finally the estimation of new drag correlation laws for poly-dispersed dilute and dense suspensions is presented.

An Efficient Simulation Method for Rare Events

Rached, Nadhir B.; Benkhelifa, Fatma; Kammoun, Abla; Alouini, Mohamed-Slim; Tempone, Raul (2015-01-07) [Poster]

Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a well-known challenging problem. Closed-form expressions for the sum distribution do not generally exist, which has led to an increasing interest in simulation approaches. A crude Monte Carlo (MC) simulation is the standard technique for the estimation of this type of probability. However, this approach is computationally expensive, especially when dealing with rare events. Variance reduction techniques are alternative approaches that can improve the computational efficiency of naive MC simulations. We propose an Importance Sampling (IS) simulation technique based on the well-known hazard rate twisting approach, that presents the advantage of being asymptotically optimal for any arbitrary RVs. The wide scope of applicability of the proposed method is mainly due to our particular way of selecting the twisting parameter. It is worth observing that this interesting feature is rarely satisfied by variance reduction algorithms whose performances were only proven under some restrictive assumptions. It comes along with a good efficiency, illustrated by some selected simulation results comparing the performance of our method with that of an algorithm based on a conditional MC technique.

A multilevel adaptive reaction-splitting method for SRNs

Moraes, Alvaro; Tempone, Raul; Vilanova, Pedro (2015-01-07) [Poster]

In this work, we present a novel multilevel Monte Carlo method for kinetic simulation of stochastic reaction networks specifically designed for systems in which the set of reaction channels can be adaptively partitioned into two subsets characterized by either “high” or “low” activity. To estimate expected values of observables of the system, our method bounds the global computational error to be below a prescribed tolerance, within a given confidence level. This is achieved with a computational complexity of order O (TOL-2).We also present a novel control variate technique which may dramatically reduce the variance of the coarsest level at a negligible computational cost. Our numerical examples show substantial gains with respect to the standard Stochastic Simulation Algorithm (SSA) by Gillespie and also our previous hybrid Chernoff tau-leap method.

Cooperative Game for Fish Harvesting and Pollution Control

Dia, Ben Mansour; Tembine, Hamidou; Tempone, Raul (2015-01-07) [Poster]

We study fishery strategies in a shallow river subject to agricultural and industrial pollution. The flowing pollutants in the river are modeled by a nonlinear stochastic differential equation in a general manner. The logistic growth model for the fish population is modified to cover the pollution impact on the fish growth rate. A stochastic cooperative game is formulated to design strategies for preserving the fish population by controlling the pollution as well as the harvesting fish.

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