Babak Farmanesh

Babak Farmanesh, Arash Pourhabib

We study large-scale spatial systems that contain exogenous variables, e.g. environmental factors that are significant predictors in spatial processes. Building predictive models for such processes is challenging because the large numbers of observations present makes it inefficient to apply full Kriging. In order to reduce computational complexity, this paper proposes Sparse Pseudo-input Local Kriging (SPLK), which utilizes hyperplanes to partition a domain into smaller subdomains and then applies a sparse approximation of the full Kriging to each subdomain. We also develop an optimization procedure to find the desired hyperplanes. To alleviate the problem of discontinuity in the global predictor, we impose continuity constraints on the boundaries of the neighboring subdomains. Furthermore, partitioning the domain into smaller subdomains makes it possible to use different parameter values for the covariance function in each region and, therefore, the heterogeneity in the data structure can be effectively captured. Numerical experiments demonstrate that SPLK outperforms, or is comparable to, the algorithms commonly applied to spatial datasets.

Babak Farmanesh, Arash Pourhabib, Balabhaskar Balasundaram et al.

We study statistical calibration, i.e., adjusting features of a computational model that are not observable or controllable in its associated physical system. We focus on functional calibration, which arises in many manufacturing processes where the unobservable features, called calibration variables, are a function of the input variables. A major challenge in many applications is that computational models are expensive and can only be evaluated a limited number of times. Furthermore, without making strong assumptions, the calibration variables are not identifiable. We propose Bayesian non-isometric matching calibration (BNMC) that allows calibration of expensive computational models with only a limited number of samples taken from a computational model and its associated physical system. BNMC replaces the computational model with a dynamic Gaussian process (GP) whose parameters are trained in the calibration procedure. To resolve the identifiability issue, we present the calibration problem from a geometric perspective of non-isometric curve to surface matching, which enables us to take advantage of combinatorial optimization techniques to extract necessary information for constructing prior distributions. Our numerical experiments demonstrate that in terms of prediction accuracy BNMC outperforms, or is comparable to, other existing calibration frameworks.