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Author Aylwin, R.; Jerez-Hanckes, C.; Schwab, C.; Zech, J.
Title Domain Uncertainty Quantification in Computational Electromagnetics Type
Year 2020 Publication Siam-Asa Journal On Uncertainty Quantification Abbreviated Journal SIAM-ASA J. Uncertain. Quantif.
Volume 8 Issue 1 Pages 301-341
Keywords computational electromagnetics; uncertainty quantification; finite elements; shape holomorphy; sparse grid quadrature; Bayesian inverse problems
Abstract We study the numerical approximation of time-harmonic, electromagnetic fields inside a lossy cavity of uncertain geometry. Key assumptions are a possibly high-dimensional parametrization of the uncertain geometry along with a suitable transformation to a fixed, nominal domain. This uncertainty parametrization results in families of countably parametric, Maxwell-like cavity problems that are posed in a single domain, with inhomogeneous coefficients that possess finite, possibly low spatial regularity, but exhibit holomorphic parametric dependence in the differential operator. Our computational scheme is composed of a sparse grid interpolation in the high-dimensional parameter domain and an Hcurl -conforming edge element discretization of the parametric problem in the nominal domain. As a stepping-stone in the analysis, we derive a novel Strang-type lemma for Maxwell-like problems in the nominal domain, which is of independent interest. Moreover, we accommodate arbitrary small Sobolev regularity of the electric field and also cover uncertain isotropic constitutive or material laws. The shape holomorphy and edge-element consistency error analysis for the nominal problem are shown to imply convergence rates for multilevel Monte Carlo and for quasi-Monte Carlo integration, as well as sparse grid approximations, in uncertainty quantification for computational electromagnetics. They also imply expression rate estimates for deep ReLU networks of shape-to-solution maps in this setting. Finally, our computational experiments confirm the presented theoretical results.
Address [Aylwin, Ruben] Pontificia Univ Catolica Chile, Sch Engn, Santiago 7820436, Chile, Email: rdaylwin@uc.cl;
Corporate Author Thesis
Publisher Siam Publications Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 2166-2525 ISBN Medium
Area Expedition Conference
Notes WOS:000551383300011 Approved
Call Number UAI @ eduardo.moreno @ Serial 1207
Permanent link to this record
 
 
Author Dölz, J.; Harbrecht, H.; Jerez-Hanckes, C.; Multerer M.
Title Isogeometric multilevel quadrature for forward and inverse random acoustic scattering Type
Year 2022 Publication Computer Methods in Applied Mechanics and Engineering Abbreviated Journal Comput. Methods in Appl. Mech. Eng.
Volume 388 Issue Pages 114242
Keywords Uncertainty quantification: Helmholtz scattering; Isogeometric Analysis; Boundary Integral Methods; Bayesian inversion; Multilevel quadrature
Abstract We study the numerical solution of forward and inverse time-harmonic acoustic scattering problems by randomly shaped obstacles in three-dimensional space using a fast isogeometric boundary element method. Within the isogeometric framework, realizations of the random scatterer can efficiently be computed by simply updating the NURBS mappings which represent the scatterer. This way, we end up with a random deformation field. In particular, we show that it suffices to know the deformation field’s expectation and covariance at the scatterer’s boundary to model the surface’s Karhunen–Loève expansion. Leveraging on the isogeometric framework, we employ multilevel quadrature methods to approximate quantities of interest such as the scattered wave’s expectation and variance. By computing the wave’s Cauchy data at an artificial, fixed interface enclosing the random obstacle, we can also directly infer quantities of interest in free space. Adopting the Bayesian paradigm, we finally compute the expected shape and variance of the scatterer from noisy measurements of the scattered wave at the artificial interface. Numerical results for the forward and inverse problems validate the proposed approach.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0045-7825 ISBN Medium
Area Expedition Conference
Notes Approved
Call Number UAI @ alexi.delcanto @ Serial 1476
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Author Escapil-Inchauspe, P.; Jerez-Hanckes, C.
Title Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Elements Approximation Type
Year 2020 Publication SIAM Journal of Scientific Computing Abbreviated Journal SIAM J. Sci. Comput.
Volume 42 Issue 5 Pages A2561-A2592
Keywords Helmholtz equation; shape calculus; uncertainty quantification; boundary element method; combination technique
Abstract We consider the numerical solution of time-harmonic acoustic scattering by obstacles with uncertain geometries for Dirichlet, Neumann, impedance, and transmission boundary conditions. In particular, we aim to quantify diffracted fields originated by small stochastic perturbations of a given relatively smooth nominal shape. Using first-order shape Taylor expansions, we derive tensor deterministic first-kind boundary integral equations for the statistical moments of the scattering problems considered. These are then approximated by sparse tensor Galerkin discretizations via the combination technique [M. Griebel, M. Schneider, and C. Zenger, A combination technique for the solution of sparse grid problems, in Iterative Methods in Linear Algebra, P. de Groen and P. Beauwens, eds., Elsevier, Amsterdam, 1992, pp. 263-281; H. Harbrecht, M. Peters, and M. Siebenmorgen, J. Comput. Phys., 252 (2013), pp. 128-141]. We supply extensive numerical experiments confirming the predicted error convergence rates with polylogarithmic growth in the number of degrees of freedom and accuracy in approximation of the moments. Moreover, we discuss implementation details such as preconditioning to finally point out further research avenues.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1064-8275 ISBN Medium
Area Expedition Conference
Notes Approved
Call Number UAI @ eduardo.moreno @ Serial 1205
Permanent link to this record
 
 
Author Faes, M.G.R.; Valdebenito, M.A.; Yuan, X.K.; Wei, P.F.; Beer, M.
Title Augmented reliability analysis for estimating imprecise first excursion probabilities in stochastic linear dynamics Type
Year 2021 Publication Advances in Engineering Software Abbreviated Journal Adv. Eng. Softw.
Volume 155 Issue Pages 102993
Keywords FAILURE PROBABILITY; SYSTEMS SUBJECT; INTERVAL; QUANTIFICATION; DESIGN
Abstract Imprecise probability allows quantifying the level of safety of a system taking into account the effect of both aleatory and epistemic uncertainty. The practical estimation of an imprecise probability is usually quite demanding from a numerical viewpoint, as it is necessary to propagate separately both types of uncertainty, leading in practical cases to a nested implementation in the so-called double loop approach. In view of this issue, this contribution presents an alternative approach that avoids the double loop by replacing the imprecise probability problem by an augmented, purely aleatory reliability analysis. Then, with the help of Bayes' theorem, it is possible to recover an expression for the failure probability as an explicit function of the imprecise parameters from the augmented reliability problem, which ultimately allows calculating the imprecise probability. The implementation of the proposed framework is investigated within the context of imprecise first excursion probability estimation of uncertain linear structures subject to imprecisely defined stochastic quantities and crisp stochastic loads. The associated augmented reliability problem is solved within the context of Directional Importance Sampling, leading to an improved accuracy at reduced numerical costs. The application of the proposed approach is investigated by means of two examples. The results obtained indicate that the proposed approach can be highly efficient and accurate.
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Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0965-9978 ISBN Medium
Area Expedition Conference
Notes WOS:000649550900002 Approved
Call Number UAI @ alexi.delcanto @ Serial 1378
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Author Fuenzalida, C.; Jerez-Hanckes, C.; McClarren, R.G.
Title Uncertainty Quantification For Multigroup Diffusion Equations Using Sparse Tensor Approximations Type
Year 2019 Publication Siam Journal On Scientific Computing Abbreviated Journal SIAM J. Sci. Comput.
Volume 41 Issue 3 Pages B545-B575
Keywords multigroup diffusion equation; uncertainty quantification; sparse tensor approximation; finite element method
Abstract We develop a novel method to compute first and second order statistical moments of the neutron kinetic density inside a nuclear system by solving the energy-dependent neutron diffusion equation. Randomness comes from the lack of precise knowledge of external sources as well as of the interaction parameters, known as cross sections. Thus, the density is itself a random variable. As Monte Carlo simulations entail intense computational work, we are interested in deterministic approaches to quantify uncertainties. By assuming as given the first and second statistical moments of the excitation terms, a sparse tensor finite element approximation of the first two statistical moments of the dependent variables for each energy group can be efficiently computed in one run. Numerical experiments provided validate our derived convergence rates and point to further research avenues.
Address [Fuenzalida, Consuelo] Pontificia Univ Catolica Chile, Sch Engn, Santiago, Chile, Email: mcfuenzalida@uc.cl;
Corporate Author Thesis
Publisher Siam Publications Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1064-8275 ISBN Medium
Area Expedition Conference
Notes WOS:000473033300033 Approved
Call Number UAI @ eduardo.moreno @ Serial 1023
Permanent link to this record
 
 
Author Morales-Bader, D.; Castillo, R.D.; Cox, R.F.A.; Ascencio-Garrido, C.
Title Parliamentary roll-call voting as a complex dynamical system: The case of Chile Type
Year 2023 Publication Plos One Abbreviated Journal PLoS One
Volume 18 Issue 4 Pages
Keywords RECURRENCE QUANTIFICATION ANALYSIS; TIME; NETWORK; WORLD
Abstract A method is proposed to study the temporal variability of legislative roll-call votes in a parliament from the perspective of complex dynamical systems. We studied the Chilean Chamber of Deputies' by analyzing the agreement ratio and the voting outcome of each vote over the last 19 years with a Recurrence Quantification Analysis and an entropy analysis (Sample Entropy). Two significant changes in the temporal variability were found: one in 2014, where the voting outcome became more recurrent and with less entropy, and another in 2018, where the agreement ratio became less recurrent and with higher entropy. These changes may be directly related to major changes in the Chilean electoral system and the composition of the Chamber of Deputies, given that these changes occurred just after the first parliamentary elections with non-compulsory voting (2013 elections) and the first elections with a proportional system in conjunction with an increase in the number of deputies (2017 elections) were held.
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Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1932-6203 ISBN Medium
Area Expedition Conference
Notes WOS:000984779900028 Approved
Call Number UAI @ alexi.delcanto @ Serial 1819
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Author Ni, P.H.; Jerez, D.J.; Fragkoulis, V.C.; Faes, M.G.R.; Valdebenito, M.A.; Beer, M.
Title Operator Norm-Based Statistical Linearization to Bound the First Excursion Probability of Nonlinear Structures Subjected to Imprecise Stochastic Loading Type
Year 2022 Publication ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A-Civil Engineering Abbreviated Journal ASCE-ASME J. Risk Uncertain. Eng. Syst. A-Civ. Eng.
Volume 8 Issue 1 Pages 04021086
Keywords Uncertainty quantification; Imprecise probabilities; Operator norm theorem; Statistical linearization
Abstract This paper presents a highly efficient approach for bounding the responses and probability of failure of nonlinear models subjected to imprecisely defined stochastic Gaussian loads. Typically, such computations involve solving a nested double-loop problem, where the propagation of the aleatory uncertainty has to be performed for each realization of the epistemic parameters. Apart from near-trivial cases, such computation is generally intractable without resorting to surrogate modeling schemes, especially in the context of performing nonlinear dynamical simulations. The recently introduced operator norm framework allows for breaking this double loop by determining those values of the epistemic uncertain parameters that produce bounds on the probability of failure a priori. However, the method in its current form is only applicable to linear models due to the adopted assumptions in the derivation of the involved operator norms. In this paper, the operator norm framework is extended and generalized by resorting to the statistical linearization methodology to
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Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 2376-7642 ISBN Medium
Area Expedition Conference
Notes WOS:000742414100022 Approved
Call Number UAI @ alexi.delcanto @ Serial 1550
Permanent link to this record