Smolyak's algorithm: A powerful black box for the acceleration of scientific computations

We provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak's work on multidimensional integration and interpolation. Since then, it has been generalized in multiple directions and has been associated with the keywords: sparse grids, hyperbolic cross approximation, combination technique, and multilevel methods. Variants of Smolyak's algorithm have been employed in the computation of high-dimensional integrals in finance, chemistry, and physics, in the numerical solution of partial and stochastic differential equations, and in uncertainty quantification. Motivated by this broad and ever-increasing range of applications, we describe a general framework that summarizes fundamental results and assumptions in a concise application-independent manner

Variance-based sensitivity analysis of oil spill predictions in the Red Sea region

To support accidental spill rapid response efforts, oil spill simulations may generally need to account for uncertainties concerning the nature and properties of the spill, which compound those inherent in model parameterizations. A full detailed account of these sources of uncertainty would however require prohibitive resources needed to sample a large dimensional space. In this work, a variance-based sensitivity analysis is conducted to explore the possibility of restricting a priori the set of uncertain parameters, at least in the context of realistic simulations of oil spills in the Red Sea region spanning a two-week period following the oil release. The evolution of the spill is described using the simulation capabilities of Modelo Hidrodinâmico, driven by high-resolution metocean fields of the Red Sea (RS) was adopted to simulate accidental oil spills in the RS. Eight spill scenarios are considered in the analysis, which are carefully selected to account for the diversity of metocean conditions in the region. Polynomial chaos expansions are employed to propagate parametric uncertainties and efficiently estimate variance-based sensitivities. Attention is focused on integral quantities characterizing the transport, deformation, evaporation and dispersion of the spill. The analysis indicates that variability in these quantities may be suitably captured by restricting the set of uncertain inputs parameters, namely the wind coefficient, interfacial tension, API gravity, and viscosity. Thus, forecast variability and confidence intervals may be reasonably estimated in the corresponding four-dimensional input space

The potential of metering roundabouts: influence in transportation externalities

Roundabouts are increasingly being used on busy arterial streets for traffic calming purposes. However, if one roundabout leg is near a distribution hub, e.g. parking areas of shopping centers, the entry traffic volumes will be particularly high in peak hours. This paper investigated a partial-metering based strategy to reduce traffic-related costs in a corridor. Specifically, the resulting traffic performance, energy, environmental and exposure impacts associated with access roundabouts were studied in an urban commercial area, namely: a) to characterize corridor operations in terms of link-specific travel time, fuel consumption, carbon dioxide and nitrogen oxides emissions, and noise costs; b) to propose an optimization model to minimize above outputs; and c) to demonstrate the model applicability under different traffic demand and directional splits combinations. Traffic, noise and vehicle dynamics data were collected from a corridor with roundabouts and signalized intersections near a commercial area of Guimarães, Portugal. Microscopic traffic and emission modeling platforms were used to model traffic operations and estimate pollutant emissions, respectively. Traffic noise was estimated with a semi-dynamical model. Link-based cost functions were developed based on the integrated modeling structure. Lastly, a Sequential quadratic programming type approach was applied to find optimal timing settings. The benefit of the partial-metering system, in terms of costs, could be up to 13% with observed traffic volumes. The efficiency of the proposed system increased as entering traffic at the metered approaches increased (~7% less costs). The findings let one to quantify metering benefits near shopping areas

Applying Bayesian model averaging for uncertainty estimation of input data in energy modelling

Background Energy scenarios that are used for policy advice have ecological and social impact on society. Policy measures that are based on modelling exercises may lead to far reaching financial and ecological consequences. The purpose of this study is to raise awareness that energy modelling results are accompanied with uncertainties that should be addressed explicitly. Methods With view to existing approaches of uncertainty assessment in energy economics and climate science, relevant requirements for an uncertainty assessment are defined. An uncertainty assessment should be explicit, independent of the assessor’s expertise, applicable to different models, including subjective quantitative and statistical quantitative aspects, intuitively understandable and be reproducible. Bayesian model averaging for input variables of energy models is discussed as method that satisfies these requirements. A definition of uncertainty based on posterior model probabilities of input variables to energy models is presented. Results The main findings are that (1) expert elicitation as predominant assessment method does not satisfy all requirements, (2) Bayesian model averaging for input variable modelling meets the requirements and allows evaluating a vast amount of potentially relevant influences on input variables and (3) posterior model probabilities of input variable models can be translated in uncertainty associated with the input variable. Conclusions An uncertainty assessment of energy scenarios is relevant if policy measures are (partially) based on modelling exercises. Potential implications of these findings include that energy scenarios could be associated with uncertainty that is presently neither assessed explicitly nor communicated adequately