图书馆订阅: Guest
Begell Digital Portal Begell 数字图书馆 电子图书 期刊 参考文献及会议录 研究收集
国际不确定性的量化期刊
影响因子: 3.259 5年影响因子: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN 打印: 2152-5080
ISSN 在线: 2152-5099

Open Access

国际不确定性的量化期刊

DOI: 10.1615/Int.J.UncertaintyQuantification.2014010728
pages 535-554

EFFECTIVE SAMPLING SCHEMES FOR BEHAVIOR DISCRIMINATION IN NONLINEAR SYSTEMS

Vu Dinh
Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, Indiana 47907, USA
Ann E. Rundell
Weldon School of Biomedical Engineering, Purdue University, 206 S. Martin Jischke Drive, West Lafayette, Indiana 47907, USA
Gregery T. Buzzard
Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, Indiana 47907, USA

ABSTRACT

Behavior discrimination is the problem of identifying sets of parameters for which the system does (or does not) reach a given set of states. While there are a variety of methods to address this problem for linear systems, few successful techniques have been developed for nonlinear models. Existing methods often rely on numerical simulations without rigorous bounds on the numerical errors and usually require a large number of model evaluations, rendering those methods impractical for studies of high-dimensional and expensive systems. In this work, we describe a probabilistic framework to estimate the boundary that separates contrasting behaviors and to quantify the uncertainty in this estimation. In our approach, we directly parameterize the, yet unknown, boundary by the zero level-set of a polynomial function, then use statistical inference on available data to identify the coefficients of the polynomial. Building upon this framework, we consider the problem of choosing effective data sampling schemes for behavior discrimination of nonlinear systems in two different settings: the low-discrepancy sampling scheme, and the uncertainty-based sequential sampling scheme. In both cases, we successfully derive theoretical results about the convergence of the expected boundary to the true boundary of interest. We then demonstrate the efficacy of the method in several application contexts with a focus on biological models. Our method outperforms previous approaches to this problem in several ways and proves to be effective to study high-dimensional and expensive systems.


Articles with similar content:

AN ADAPTIVE REDUCED BASIS COLLOCATION METHOD BASED ON PCM ANOVA DECOMPOSITION FOR ANISOTROPIC STOCHASTIC PDES
International Journal for Uncertainty Quantification, Vol.8, 2018, issue 3
Heyrim Cho, Howard C. Elman
IMPROVEMENTS TO GRADIENT-ENHANCED KRIGING USING A BAYESIAN INTERPRETATION
International Journal for Uncertainty Quantification, Vol.4, 2014, issue 3
Hester Bijl, Richard P. Dwight, Jouke H.S. de Baar
DIMENSIONALITY REDUCTION FOR COMPLEX MODELS VIA BAYESIAN COMPRESSIVE SENSING
International Journal for Uncertainty Quantification, Vol.4, 2014, issue 1
Bert J. Debusschere, Habib N. Najm, Peter Thornton, Cosmin Safta, Khachik Sargsyan, Daniel Ricciuto
OPTIMIZATION-BASED SAMPLING IN ENSEMBLE KALMAN FILTERING
International Journal for Uncertainty Quantification, Vol.4, 2014, issue 4
Alexander Bibov, Heikki Haario, Antti Solonen, Johnathan M. Bardsley
BIAS MINIMIZATION IN GAUSSIAN PROCESS SURROGATE MODELING FOR UNCERTAINTY QUANTIFICATION
International Journal for Uncertainty Quantification, Vol.1, 2011, issue 4
Vadiraj Hombal, Sankaran Mahadevan