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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
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Author Bergen, M.; Munoz, F.D.
Title Quantifying the effects of uncertain climate and environmental policies on investments and carbon emissions: A case study of Chile Type
Year 2018 Publication Energy Economics Abbreviated Journal Energy Econ.
Volume 75 Issue Pages 261-273
Keywords Uncertainty; Climate policies; Transmission and generation planning; Carbon emissions; Stochastic programming; Equilibrium
Abstract In this article we quantify the effect of uncertainty of climate and environmental policies on transmission and generation investments, as well as on CO2 emissions in Chile. We use a two-stage stochastic planning model with recourse or corrective investment options to find optimal portfolios of infrastructure both under perfect information and uncertainty. Under a series of assumptions, this model is equivalent to the equilibrium of a much more complicated bi-level market model, where a transmission planner chooses investments first and generation firms invest afterwards. We find that optimal investment strategies present important differences depending on the policy scenario. By changing our assumption of how agents will react to this uncertainty we compute bounds on the cost that this uncertainty imposes on the system, which we estimate ranges between 3.2% and 5.7% of the minimum expected system cost of $57.6B depending on whether agents will consider or not uncertainty when choosing investments. We also find that, if agents choose investments using a stochastic planning model, uncertain climate policies can result in nearly 18% more CO2 emissions than the equilibrium levels observed under perfect information. Our results highlight the importance of credible and stable long-term regulations for investors in the electric power industry if the goal is to achieve climate and environmental targets in the most cost-effective manner and to minimize the risk of asset stranding. (C) 2018 Elsevier B.V. All rights reserved.
Address [Bergen, Matias] Politecn Torino, Turin, Italy, Email: mebergen@uc.cl;
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0140-9883 ISBN Medium
Area Expedition Conference
Notes WOS:000449891600019 Approved
Call Number UAI @ eduardo.moreno @ Serial 930
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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
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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
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Author Guevara, E.; Babonneau, F.; Homem-de-Mello, T.; Moret, S.
Title A machine learning and distributionally robust optimization framework for strategic energy planning under uncertainty Type
Year 2020 Publication Applied Energy Abbreviated Journal Appl. Energy
Volume 271 Issue Pages 18 pp
Keywords Strategic energy planning; Electricity generation; Uncertainty; Distributionally robust optimization; Machine learning
Abstract This paper investigates how the choice of stochastic approaches and distribution assumptions impacts strategic investment decisions in energy planning problems. We formulate a two-stage stochastic programming model assuming different distributions for the input parameters and show that there is significant discrepancy among the associated stochastic solutions and other robust solutions published in the literature. To remedy this sensitivity issue, we propose a combined machine learning and distributionally robust optimization (DRO) approach which produces more robust and stable strategic investment decisions with respect to uncertainty assumptions. DRO is applied to deal with ambiguous probability distributions and Machine Learning is used to restrict the DRO model to a subset of important uncertain parameters ensuring computational tractability. Finally, we perform an out-of-sample simulation process to evaluate solutions performances. The Swiss energy system is used as a case study all along the paper to validate the approach.
Address [Guevara, Esnil] Univ Adolfo Ibanez, PhD Program Ind Engn & Operat Res, Santiago, Chile, Email: frederic.babonneau@uai.cl
Corporate Author Thesis
Publisher Elsevier Sci Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0306-2619 ISBN Medium
Area Expedition Conference
Notes WOS:000540436500003 Approved
Call Number UAI @ eduardo.moreno @ Serial 1188
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Author Lagos, G.; Espinoza, D.; Moreno, E.; Vielma, J.P.
Title Restricted risk measures and robust optimization Type
Year 2015 Publication European Journal Of Operational Research Abbreviated Journal Eur. J. Oper. Res.
Volume 241 Issue 3 Pages 771-782
Keywords Risk management; Stochastic programming; Uncertainty modeling
Abstract In this paper we consider characterizations of the robust uncertainty sets associated with coherent and distortion risk measures. In this context we show that if we are willing to enforce the coherent or distortion axioms only on random variables that are affine or linear functions of the vector of random parameters, we may consider some new variants of the uncertainty sets determined by the classical characterizations. We also show that in the finite probability case these variants are simple transformations of the classical sets. Finally we present results of computational experiments that suggest that the risk measures associated with these new uncertainty sets can help mitigate estimation errors of the Conditional Value-at-Risk. (C) 2014 Elsevier B.V. All rights reserved.
Address [Lagos, Guido] Georgia Inst Technol, H Milton Stewart Sch Ind & Syst Engn, Atlanta, GA 30332 USA, Email: glagos@gatech.edu;
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0377-2217 ISBN Medium
Area Expedition Conference
Notes WOS:000347605100018 Approved
Call Number UAI @ eduardo.moreno @ Serial 438
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Author O' Ryan, R.; Benavides, C.; Diaz, M.; San Martin, J.P.; Mallea, J.
Title Using probabilistic analysis to improve greenhouse gas baseline forecasts in developing country contexts: the case of Chile Type
Year 2019 Publication Climate Policy Abbreviated Journal Clim. Policy
Volume 19 Issue 3 Pages 299-314
Keywords Energy systems modelling; uncertainty; climate change policy; probabilistic analysis; emission baselines; nationally determined contributions
Abstract In this paper, initial steps are presented toward characterizing, quantifying, incorporating and communicating uncertainty applying a probabilistic analysis to countrywide emission baseline forecasts, using Chile as a case study. Most GHG emission forecasts used by regulators are based on bottom-up deterministic approaches. Uncertainty is usually incorporated through sensitivity analysis and/or use of different scenarios. However, much of the available information on uncertainty is not systematically included. The deterministic approach also gives a wide range of variation in values without a clear sense of probability of the expected emissions, making it difficult to establish both the mitigation contributions and the subsequent policy prescriptions for the future. To improve on this practice, we have systematically included uncertainty into a bottom-up approach, incorporating it in key variables that affect expected GHG emissions, using readily available information, and establishing expected baseline emissions trajectories rather than scenarios. The resulting emission trajectories make explicit the probability percentiles, reflecting uncertainties as well as possible using readily available information in a manner that is relevant to the decision making process. Additionally, for the case of Chile, contradictory deterministic results are eliminated, and it is shown that, whereas under a deterministic approach Chile's mitigation ambition does not seem high, the probabilistic approach suggests this is not necessarily the case. It is concluded that using a probabilistic approach allows a better characterization of uncertainty using existing data and modelling capacities that are usually weak in developing country contexts. Key policy insights Probabilistic analysis allows incorporating uncertainty systematically into key variables for baseline greenhouse gas emission scenario projections. By using probabilistic analysis, the policymaker can be better informed as to future emission trajectories. Probabilistic analysis can be done with readily available data and expertise, using the usual models preferred by policymakers, even in developing country contexts.
Address [O' Ryan, Raul] Univ Adolfo Ibanez, Fac Engn & Sci, EARTH Ctr, Santiago, Chile, Email: mdiaz@centroenergia.cl
Corporate Author Thesis
Publisher Taylor & Francis Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1469-3062 ISBN Medium
Area Expedition Conference
Notes WOS:000455949300003 Approved
Call Number UAI @ eduardo.moreno @ Serial 1164
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Author Pereira, J.
Title The robust (minmax regret) single machine scheduling with interval processing times and total weighted completion time objective Type
Year 2016 Publication Computers & Operations Research Abbreviated Journal Comput. Oper. Res.
Volume 66 Issue Pages 141-152
Keywords Scheduling; Single machine; Uncertainty; Robust optimization; Branch-and-bound
Abstract Single machine scheduling is a classical optimization problem that depicts multiple real life systems in which a single resource (the machine) represents the whole system or the bottleneck operation of the system. In this paper we consider the problem under a weighted completion time performance metric in which the processing time of the tasks to perform (the jobs) are uncertain, but can only take values from closed intervals. The objective is then to find a solution that minimizes the maximum absolute regret for any possible realization of the processing times. We present an exact branch-and-bound method to solve the problem, and conduct a computational experiment to ascertain the possibilities and limitations of the proposed method. The results show that the algorithm is able to optimally solve instances of moderate size (25-40 jobs depending on the characteristics of the instance). (c) 2015 Elsevier Ltd. All rights reserved.
Address [Pereira, Jordi] Univ Adolfo Ibanez, Fac Sci & Engn, Vina Del Mar, Chile, Email: jorge.pereira@uai.cl
Corporate Author Thesis
Publisher Pergamon-Elsevier Science Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0305-0548 ISBN Medium
Area Expedition Conference
Notes WOS:000366779900013 Approved
Call Number UAI @ eduardo.moreno @ Serial 558
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Author Ramirez-Sagner, G.; Munoz, F.D.
Title The effect of head-sensitive hydropower approximations on investments and operations in planning models for policy analysis Type
Year 2019 Publication Renewable & Sustainable Energy Reviews Abbreviated Journal Renew. Sust. Energ. Rev.
Volume 105 Issue Pages 38-47
Keywords Generation planning; Hydropower; Policy analysis; Simplifications; Uncertainty
Abstract Planning for new generation infrastructure in hydrothermal power systems requires consideration of a series of nonlinearities that are often ignored in planning models for policy analysis. In this article, three different capacity- planning models are used, one nonlinear and two linear ones, with different degrees of complexity, to quantify the impact of simplifying the head dependency of hydropower generation on investments in both conventional and renewable generators and system operations. It was found that simplified investment models can bias the optimal generation portfolios by, for example, understating the need for coal and combined-cycle gas units and overstating investments in wind capacity with respect to a more accurate nonlinear formulation, which could affect policy recommendations. It was also found that the economic cost of employing a simplified model can be below 10% of total system cost for most of the scenarios and system configurations analyzed, but as high as nearly 70% of total system cost for specific applications. Although these results are not general, they suggest that for certain system configurations both linear models can provide reasonable approximations to more complex nonlinear formulations. Uncertain water inflows were also considered using stochastic variants of all three planning models. Interestingly, if due to time or computational limitations only one of these two features could be accounted for, these results indicate that explicit modeling of the nonlinear-head effect in a deterministic model could yield better results (up to 0.6% of economic regret) than a stochastic linear model (up to 9.6% of economic regret) that considers the uncertainty of water inflows.
Address [Ramirez-Sagner, Gonzalo] Fraunhofer Chile Res, Ctr Solar Energy Technol, Santiago, Chile, Email: grramire@uc.cl;
Corporate Author Thesis
Publisher Pergamon-Elsevier Science Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1364-0321 ISBN Medium
Area Expedition Conference
Notes WOS:000460121000003 Approved
Call Number UAI @ eduardo.moreno @ Serial 988
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Author Reus, L.; Belbeze, M.; Feddersen, H.; Rubio, E.
Title Extraction Planning Under Capacity Uncertainty at the Chuquicamata Underground Mine Type
Year 2018 Publication Interfaces Abbreviated Journal Interfaces
Volume 48 Issue 6 Pages 543-555
Keywords underground mine extraction scheduling; operational uncertainty management; stochastic programming applications; long-term mine planning
Abstract We propose an extraction schedule for the Chuquicamata underground copper mine in Chile. The schedule maximizes profits while adhering to all operational and geomechanical requirements involved in proper removal of the material. We include extraction capacity uncertainties due to failure in equipment, specifically to the overland conveyor, which we find to be the most critical component in the extraction process. First we present the extraction plan based on a deterministic model, which does not assume uncertainty in the extraction capacity and represents the solution that the mine can implement without using the results of this study. Then we extend this model to a stochastic setting by generating different scenarios for capacity values in subsequent periods. We construct a multistage model that handles economic downside risk arising from this uncertainty by penalizing plans that deviate from an ex ante profit target in one or more scenarios. Simulation results show that a stochastic-based solution can achieve the same expected profits as the deterministic-based solution. However, the earnings of the stochastic-based solution average 5% more for scenarios in which earnings are below the 10th percentile. If we choose a target 2% below the expected profit obtained by the deterministic-based solution, this average increases from 5% to 9%.
Address [Reus, Lorenzo; Belbeze, Mathias; Feddersen, Hans] Adolfo Ibanez Univ, Dept Engn & Sci, Santiago 7910000, Chile, Email: lorenzo.reus@uai.cl;
Corporate Author Thesis
Publisher Informs Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0092-2102 ISBN Medium
Area Expedition Conference
Notes WOS:000454513500005 Approved
Call Number UAI @ eduardo.moreno @ Serial 967
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Author Vogt-Geisse, K.; Lorenzo, C.; Feng, Z.L.
Title Impact Of Age-Dependent Relapse And Immunity On Malaria Dynamics Type
Year 2013 Publication Journal Of Biological Systems Abbreviated Journal J. Biol. Syst.
Volume 21 Issue 4 Pages 49 pp
Keywords Malaria; Endemic Model; Age-structure; Reproductive Number; Uncertainty and Sensitivity Analysis
Abstract An age-structured mathematical model for malaria is presented. The model explicitly includes the human and mosquito populations, structured by chronological age of humans. The infected human population is divided into symptomatic infectious, asymptomatic infectious and asymptomatic chronic infected individuals. The original partial differential equation (PDE) model is reduced to an ordinary differential equation (ODE) model with multiple age groups coupled by aging. The basic reproduction number R-0 is derived for the PDE model and the age group model in the case of general n age groups. We assume that infectiousness of chronic infected individuals gets triggered by bites of even susceptible mosquitoes. Our analysis points out that this assumption contributes greatly to the R0 expression and therefore needs to be further studied and understood. Numerical simulations for n = 2 age groups and a sensitivity/uncertainty analysis are presented. Results suggest that it is important not only to consider asymptomatic infectious individuals as a hidden cause for malaria transmission, but also asymptomatic chronic infections (>60%), which often get neglected due to undetectable parasite loads. These individuals represent an important reservoir for future human infectiousness. By considering age-dependent immunity types, the model helps generate insight into effective control measures, by targeting age groups in an optimal way.
Address [Vogt-Geisse, Katia; Lorenzo, Christina; Feng, Zhilan] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA, Email: kvogtgei@math.purdue.edu;
Corporate Author Thesis
Publisher World Scientific Publ Co Pte Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0218-3390 ISBN Medium
Area Expedition Conference
Notes WOS:000331243400002 Approved
Call Number UAI @ eduardo.moreno @ Serial 351
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