Coordinate Transformation and Polynomial Chaos for the Bayesian Inference of a Gaussian Process with Parametrized Prior Covariance Function

This paper addresses model dimensionality reduction for Bayesian inference based on prior Gaussian fields with uncertainty in the covariance function hyper-parameters. The dimensionality reduction is traditionally achieved using the Karhunen-\Loeve expansion of a prior Gaussian process assuming covariance function with fixed hyper-parameters, despite the fact that these are uncertain in nature. The posterior distribution of the Karhunen-Lo\`{e}ve coordinates is then inferred using available observations. The resulting inferred field is therefore dependent on the assumed hyper-parameters. Here, we seek to efficiently estimate both the field and covariance hyper-parameters using Bayesian inference. To this end, a generalized Karhunen-Lo\`{e}ve expansion is derived using a coordinate transformation to account for the dependence with respect to the covariance hyper-parameters. Polynomial Chaos expansions are employed for the acceleration of the Bayesian inference using similar coordinate transformations, enabling us to avoid expanding explicitly the solution dependence on the uncertain hyper-parameters. We demonstrate the feasibility of the proposed method on a transient diffusion equation by inferring spatially-varying log-diffusivity fields from noisy data. The inferred profiles were found closer to the true profiles when including the hyper-parameters' uncertainty in the inference formulation.Comment: 34 pages, 17 figure

Self-Propagating Reactive Fronts in Compacts of Multilayered Particles

Reactive multilayered foils in the form of thin films have gained interest in various applications such as joining, welding, and ignition. Typically, thin film multilayers support self-propagating reaction fronts with speeds ranging from 1 to 20 m/s. In some applications, however, reaction fronts with much smaller velocities are required. This recently motivated Fritz et al. (2011) to fabricate compacts of regular sized/shaped multilayered particles and demonstrate self-sustained reaction fronts having much smaller velocities than thin films with similar layering. In this work, we develop a simplified numerical model to simulate the self-propagation of reactive fronts in an idealized compact, comprising identical Ni/Al multilayered particles in thermal contact. The evolution of the reaction in the compact is simulated using a two-dimensional transient model, based on a reduced description of mixing, heat release, and thermal transport. Computed results reveal that an advancing reaction front can be substantially delayed as it crosses from one particle to a neighboring particle, which results in a reduced mean propagation velocity. A quantitative analysis is thus conducted on the dependence of these phenomena on the contact area between the particles, the thermal contact resistance, and the arrangement of the multilayered particles

A priori testing of sparse adaptive polynomial chaos expansions using an ocean general circulation model database

This work explores the implementation of an adaptive strategy to design sparse ensembles of oceanic simulations suitable for constructing polynomial chaos surrogates. We use a recently developed pseudo-spectral algorithm that is based on a direct application of the Smolyak sparse grid formula and that allows the use of arbitrary admissible sparse grids. The adaptive algorithm is tested using an existing simulation database of the oceanic response to Hurricane Ivan in the Gulf of Mexico. The a priori tests demonstrate that sparse and adaptive pseudo-spectral constructions lead to substantial savings over isotropic sparse sampling in the present setting.United States. Office of Naval Research (award N00014-101-0498)United States. Dept. of Energy. Office of Advanced Scientific Computing Research (award numbers DE-SC0007020, DE-SC0008789, and DE-SC0007099)Gulf of Mexico Research Initiative (contract numbers SA1207GOMRI005 (CARTHE) and SA12GOMRI008 (DEEP-C)

Turismo acessível para todos, um paradigma emergente e um desafio para a oferta turística. O caso dos espaços museológicos e empreendimentos turísticos de Cascais.

Reflexão sobre o turismo acessível para todos, como modelo que se revela cada vez mais essencial para todo o sistema turístico, que se afirma não só pela sua relevância social, cívica e demográfica mas também pelas potencialidades económicas associadas. Todavia, o turismo acessível constitui um desafio de adaptação para a oferta turística instalada há vários anos, em destinos turísticos mais antigos, como é o caso de Cascais.Reflection on accessible tourism for all, as an increasingly essential model for the touristic system, that claims not only for its social, civic and demographic significance, but also for the economic potential associated. However, the accessible tourism is an adaptation challenge for the elderly tourism supply, at long-established tourism destinations, such as Cascais

Changing climate both increases and decreases European river floods

Climate change has led to concerns about increasing river floods resulting from the greater water-holding capacity of a warmer atmosphere1. These concerns are reinforced by evidence of increasing economic losses associated with flooding in many parts of the world, including Europe2. Any changes in river floods would have lasting implications for the design of flood protection measures and flood risk zoning. However, existing studies have been unable to identify a consistent continental-scale climatic-change signal in flood discharge observations in Europe3, because of the limited spatial coverage and number of hydrometric stations. Here we demonstrate clear regional patterns of both increases and decreases in observed river flood discharges in the past five decades in Europe, which are manifestations of a changing climate. Our results\u2014arising from the most complete database of European flooding so far\u2014suggest that: increasing autumn and winter rainfall has resulted in increasing floods in northwestern Europe; decreasing precipitation and increasing evaporation have led to decreasing floods in medium and large catchments in southern Europe; and decreasing snow cover and snowmelt, resulting from warmer temperatures, have led to decreasing floods in eastern Europe. Regional flood discharge trends in Europe range from an increase of about 11 per cent per decade to a decrease of 23 per cent. Notwithstanding the spatial and temporal heterogeneity of the observational record, the flood changes identified here are broadly consistent with climate model projections for the next century4,5, suggesting that climate-driven changes are already happening and supporting calls for the consideration of climate change in flood risk management

Drag Parameter Estimation Using Gradients and Hessian from a Polynomial Chaos Model Surrogate

Abstract A variational inverse problem is solved using polynomial chaos expansions to infer several critical variables in the Hybrid Coordinate Ocean Model’s (HYCOM’s) wind drag parameterization. This alternative to the Bayesian inference approach in Sraj et al. avoids the complications of constructing the full posterior with Markov chain Monte Carlo sampling. It focuses instead on identifying the center and spread of the posterior distribution. The present approach leverages the polynomial chaos series to estimate, at very little extra cost, the gradients and Hessian of the cost function during minimization. The Hessian’s inverse yields an estimate of the uncertainty in the solution when the latter’s probability density is approximately Gaussian. The main computational burden is an ensemble of realizations to build the polynomial chaos expansion; no adjoint code or additional forward model runs are needed once the series is available. The ensuing optimal parameters are compared to those obtained in Sraj et al. where the full posterior distribution was constructed. The similarities and differences between the new methodology and a traditional adjoint-based calculation are discussed