2012/12/31 by Xun Huan, Youssef Marzouk, Youssef M. Marzouk · 115 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Applied mathematics #Computer science #Estimator #Gaussian Processes and Bayesian Inference #Mathematical optimization #Mathematics #Monte Carlo method #Nonlinear system #Probabilistic and Robust Engineering Design #Robustness (evolution) #Statistics #Stochastic approximation #Stochastic optimization #math.OC #stat.CO #stat.ME
paper · pdf · doi:10.1615/int.j.uncertaintyquantification.2014006730
published in International Journal for Uncertainty Quantification 4(6), 479-510 (Begell House) · Preprint 40 pages, 10 figures (121 small figures). v1 submitted to the International Journal for Uncertainty Quantification on December 10, 2012; v2 submitted on September 10, 2013. v2 changes: (a) clarified algorithm stopping criteria and other parameters; (b) emphasized paper contributions, plus other minor edits; v3 submitted on December 26, 2014. v3 changes: minor edits
openalex publication_date 2014/01/01 · arxiv created 2014/12/26 · arxiv updated 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Optimal experimental design (OED) seeks experiments expected to yield the most useful data for some purpose. In practical circumstances where experiments are time-consuming or resource-intensive, OED can yield enormous savings. We pursue OED for nonlinear systems from a Bayesian perspective, with the goal of choosing experiments that are optimal for parameter inference. Our objective in this context is the expected information gain in model parameters, which in general can only be estimated using Monte Carlo methods. Maximizing this objective thus becomes a stochastic optimization problem. This paper develops gradient-based stochastic optimization methods for the design of experi-ments on a continuous parameter space. Given a Monte Carlo estimator of expected information gain, we use infinitesimal perturbation analysis to derive gradients of this estimator. We are then able to formulate two gradient-based stochastic optimization approaches: (i) Robbins-Monro stochastic approximation, and (ii) sample average approximation combined with a determinis-tic quasi-Newton method. A polynomial chaos approximation of the forward model accelerates objective and gradient evaluations in both cases. We discuss the implementation of these opti-mization methods, then conduct an empirical comparison of their performance. To demonstrate design in a nonlinear setting with partial differential equation forward models, we use the prob-lem of sensor placement for source inversion. Numerical results yield useful guidelines on the choice of algorithm and sample sizes, assess the impact of estimator bias, and quantify tradeoffs of computational cost versus solution quality and robustness. 1