Fast Bayesian Optimal Experimental Design for Seismic Source Inversion(2016-01-06) Long, Quan; Motamed, Mohammad; Tempone, Raul; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; United Technologies Research Center; University of New Mexico
We develop a fast method for optimally designing experiments  in the context of statistical seismic source inversion . In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by the elastic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the true parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem.
A Sparsity-Regularized Reconstruction of Two-Dimensional Piecewise Continuous Domains!(2016-01-06) Sandhu, Ali Imran; Desmal, Abdulla; Bagci, Hakan; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Electrical Engineering Program
Multiscale Modeling of Wear Degradation(2016-01-06) Moraes, Alvaro; Ruggeri, Fabrizio; Tempone, Raul; Vilanova, Pedro; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Istituto di Matematica Applicata e Tecnologie Informatiche
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 , 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 in Random Microstructures: a Multilevel Monte Carlo Approach(2016-01-06) Icardi, Matteo; Tempone, Raul; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; University of Warwick
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.