Uncertainty Updating in the Description of Coupled Heat and Moisture Transport in Heterogeneous Materials

To assess the durability of structures, heat and moisture transport need to be analyzed. To provide a reliable estimation of heat and moisture distribution in a certain structure, one needs to include all available information about the loading conditions and material parameters. Moreover, the information should be accompanied by a corresponding evaluation of its credibility. Here, the Bayesian inference is applied to combine different sources of information, so as to provide a more accurate estimation of heat and moisture fields [1]. The procedure is demonstrated on the probabilistic description of heterogeneous material where the uncertainties consist of a particular value of individual material characteristic and spatial fluctuations. As for the heat and moisture transfer, it is modelled in coupled setting [2]

EigenGP: Gaussian Process Models with Adaptive Eigenfunctions

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both basis dictionary elements--eigenfunctions of a GP prior--and prior precisions in a sparse finite model. It is well known that, among all orthogonal basis functions, eigenfunctions can provide the most compact representation. Unlike other sparse Bayesian finite models where the basis function has a fixed form, our eigenfunctions live in a reproducing kernel Hilbert space as a finite linear combination of kernel functions. We learn the dictionary elements--eigenfunctions--and the prior precisions over these elements as well as all the other hyperparameters from data by maximizing the model marginal likelihood. We explore computational linear algebra to simplify the gradient computation significantly. Our experimental results demonstrate improved predictive performance of EigenGP over alternative sparse GP methods as well as relevance vector machine.Comment: Accepted by IJCAI 201

Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems

Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting estimates become inaccurate. One can improve the accuracy by adaptively increasing the order of the polynomial chaos, but the cost may increase too fast for this to be cost effective compared to Monte Carlo sampling without a surrogate posterior

Computational design of patterned interfaces using reduced order models

Patterning is a familiar approach for imparting novel functionalities to free surfaces. We extend the patterning paradigm to interfaces between crystalline solids. Many interfaces have non-uniform internal structures comprised of misfit dislocations, which in turn govern interface properties. We develop and validate a computational strategy for designing interfaces with controlled misfit dislocation patterns by tailoring interface crystallography and composition. Our approach relies on a novel method for predicting the internal structure of interfaces: rather than obtaining it from resource-intensive atomistic simulations, we compute it using an efficient reduced order model based on anisotropic elasticity theory. Moreover, our strategy incorporates interface synthesis as a constraint on the design process. As an illustration, we apply our approach to the design of interfaces with rapid, 1-D point defect diffusion. Patterned interfaces may be integrated into the microstructure of composite materials, markedly improving performance.United States. Dept. of Energy. Office of Basic Energy Sciences (Award 2008LANL1026)National Science Foundation (U.S.) (Grant 1150862