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International Journal for Uncertainty Quantification
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ISSN Imprimer: 2152-5080
ISSN En ligne: 2152-5099

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International Journal for Uncertainty Quantification

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

RÉSUMÉ

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.


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