Scalable Algorithms for Uncertainty Quantification and Bayesian Inference with Applications to Computational Mechanics

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The proposed statistical framework intends to provide a rational approach to reconciling running computational simulations with measurement data in uncertain and rapidly changing environments for accurate and realistic numerical predictions for informed and optimal decision-making. The long-term objective of the proposed research is to develope uncertainty quantification, data assimilation and model selection algorithms which can exploit the extreme-scale parallelism required to effectively leverage petascale and future exascale systems with millions of cores and accelerators (e.g. graphics processing units and coprocessors). The proposed algorithms will be applied to tackle computational stochastic mechanics problems related to (a) real-time nonlinear aeroelastic computations using streaming wind-tunnel data; (b) uncertainty quantification in middle frequency structural dynamics; and (c) nonlinear (elasto-plastic) seismic wave propagations through random geological media. The novelties of the proposed research are: (1) the mathematical formulation and distributed implemention of MH-MCMC algorithms for Bayesian parameter estimation and model selection in conjunction with its experimental validation for nonlinear aeroelastic computation using streaming wind-tunnel data; and (2) the development of an intrusive polynomial chaos-based multi-level domain decomposition algorithm for SPDES for ultra-scale computations in petascale/future exascale systems, along with its applications to the middle frequency structural dynamics and elasto-plastic seismic wave propagation in random soil strata. The uncertainty quantification and data assimilation in computational models will boost public confidence and regulatory acceptance in order to assess the safety and reliability of engineering systems for aeroelastic performance of long-span bridges, air vehicles, seismic risk assessment of dams and nuclear reactors and, detection of military activities from seismic signatures. The proposed Bayesian estimation framework for computional modeling can bridge the gap between experimentalists and numerical modelers in various disciplines in science and engineering. Capitalizing on the investments in large-scale national computing facilities, the proposed research initiatives will offer technological leadership to Canada including the development of a highly skilled workforce capable of high performance computing, uncertainty quantification and statistical inference relevant to computational and data science applications.