Analyticity and Sparsity in Uncertainty Quantification for Pdes with Gaussian Random Field Inputs

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About this book The present book develops the mathematical and numerical analysis of linear, elliptic and parabolic partial differential equations (PDEs) with coefficients whose logarithms are modelled as Gaussian random fields (GRFs), in polygonal and polyhedral physical domains. Both, forward and Bayesian inverse PDE problems subject to GRF priors are considered. Adopting a pathwise, affine-parametric representation of the GRFs, turns the random PDEs into equivalent, countably-parametric, deterministic PDEs, with nonuniform ellipticity constants. A detailed sparsity analysis of Wiener-Hermite polynomial chaos expansions of the corresponding parametric PDE solution families by analytic continuation into the complex domain is developed, in corner- and edge-weighted function spaces on the physical domain. The presented Algorithms and results are relevant for the mathematical analysis of many approximation methods for PDEs with GRF inputs, such as model order reduction, neural network and tensor-formatted surrogates of parametric solution families. They are expected to impact computational uncertainty quantification subject to GRF models of uncertainty in PDEs, and are of interest for researchers and graduate students in both, applied and computational mathematics, as well as in computational science and engineering.

Navigating Uncertainty in the South China Sea Disputes

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This collaborative and edited volume explores the geopolitical and geostrategic significance of the South China Sea disputes. Experts from interdisciplinary fields and knowledge analyze the South China Sea's historical and contemporary strategic significance alongside the dynamics of evolving political powers in Asia. Overall, Navigating Uncertainty in the South China Sea Disputes explains why this issue resonates on a global scale and where it will move from here. This book explores a complex conflict challenging democracy, patriotism, resources, power, and the nature of Asia's future identity. With the increasing demand for natural resources in the region, it is becoming difficult to maintain a balanced and humanistic approach on the global stage. Navigating Uncertainty in the South China Sea Disputes will answer two key questions: first, why the South China Sea is of vital importance to Asia-Pacific nations; second, cover the interests of external powers and explain what international laws apply to the South China Sea, detailing rules that all parties should follow. By focusing attention on these issues, we hope to encourage scholars to expand the range of texts and genres they are willing to explore in search of nuanced ideas and debates.