DAE 2024 - Session VIII

Session VIII (May 16, 3:30pm-5:00pm): Design Issues in Uncertainty Quantification, organized by Robert Gramacy

Title: Deep Gaussian Process Surrogates for Contour Location and Reliability Analysis
Speaker: Annie S. Booth, NC State University
Abstract: Bayesian deep Gaussian processes (DGPs) outperform ordinary GPs as surrogate models of complex computer experiments when response surface dynamics are non-stationary. Reliability analysis through contour location is a common downstream task, but DGP surrogates have not been deployed in this area. Level sets separating passable vs. failable operating conditions are best learned through strategic sequential design. There are two limitations to modern CL methodology which hinder DGP integration in this setting. First, derivative-based optimization underlying acquisition functions is thwarted by sampling-based Bayesian (i.e., MCMC) inference, which is essential for DGP posterior integration. Second, canonical acquisition criteria, such as entropy, are famously myopic to the extent that optimization may even be undesirable. Here we tackle both of these limitations at once, proposing a hybrid criteria that explores along the Pareto front of entropy and (predictive) uncertainty, requiring evaluation only at strategically located “triangulation” candidates. We showcase DGP CL performance in several synthetic benchmark exercises and on a real-world RAE-2822 transonic airfoil simulation.

Title: Sequential Bayesian Experimental Design for Calibration of Expensive Simulation Models
Speaker: Ozge Surer, Miami University (OH)
Abstract: Simulation models of critical systems often have parameters that need to be calibrated using observed data. For expensive simulation models, calibration is done using an emulator of the simulation model built on simulation output at different parameter settings. Using intelligent and adaptive selection of parameters to build the emulator can drastically improve the efficiency of the calibration process. In this talk, I will present a sequential framework with a novel criterion for parameter selection that targets learning the posterior density of the parameters. The emergent behavior from this criterion is that exploration happens by selecting parameters in uncertain posterior regions while simultaneously exploitation happens by selecting parameters in regions of high posterior density. The advantages of the proposed method are illustrated using several simulation experiments and a nuclear physics reaction model.

Title: Scalable Bayesian Optimization for Noisy Problems
Speaker: Mickael Binois, INRIA
Abstract: Stochastic simulators may exhibit low signal-to-noise ratios, hence requiring large budget of evaluations to find accurate solutions. For deterministic and high signal to noise ratio problems, Bayesian optimization is a sample efficient technique. In particular, recent works have shown the interest of combining it with trust region methods to help convergence. Here we revisit this combination for noisier problems, when the number of evaluations may reach millions or even billions. We build upon local heteroscedastic Gaussian process modeling to adapt to both noise and nonstationarity, while adapting the degree of replication at each design to scale with respect to the number of observations. In particular, our method is able to identify solutions with an arbitrary precision. We illustrate our method on several synthetic test cases, as well as some more realistic ones.