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: 0.531 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.2012003722
pages 47-71

PHYSICS-BASED COVARIANCE MODELS FOR GAUSSIAN PROCESSES WITH MULTIPLE OUTPUTS

Emil M. Constantinescu
Mathematics and Computer Science Division, Argonne National Laboratory, USA
Mihai Anitescu
Mathematics and Computer Science Division, Argonne National Laboratory, USA

ABSTRACT

Gaussian process analysis of processes with multiple outputs is limited by the fact that far fewer good classes of covariance functions exist compared with the scalar (single-output) case. To address this difficulty, we turn to covariance function models that take a form consistent in some sense with physical laws that govern the underlying simulated process. Models that incorporate such information are suitable when performing uncertainty quantification or inferences on multidimensional processes with partially known relationships among different variables, also known as cokriging. One example is in atmospheric dynamics where pressure and wind speed are driven by geostrophic assumptions (wind ∝ ∂/∂x pressure). In this study we develop both analytical and numerical auto-covariance and cross-covariance models that are consistent with physical constraints or can incorporate automatically sensible assumptions about the process that generated the data. We also determine high-order closures, which are required for nonlinear dependencies among the observables. We use these models to study Gaussian process regression for processes with multiple outputs and latent processes (i.e., processes that are not directly observed and predicted but inter-relate the output quantities). Our results demonstrate the effectiveness of the approach on both synthetic and real data sets.


Articles with similar content:

A NOVEL TWO-PARAMETER RELATIVE PERMEABILITY MODEL
Journal of Porous Media, Vol.15, 2012, issue 11
Seyed Hamed Bolouri, Eshragh Ghoodjani
Reconstructed Structures in the Problems of Control and Investigation of Surface Images Processing Algorithms for Evaluating Solid-Body Deformations
Telecommunications and Radio Engineering, Vol.68, 2009, issue 9
N. I. Ksenev, S. V. Shidlovskii, V. I. Syryamkin
APPROXIMATE LEVEL-CROSSING PROBABILITIES FOR INTERACTIVE VISUALIZATION OF UNCERTAIN ISOCONTOURS
International Journal for Uncertainty Quantification, Vol.3, 2013, issue 2
Christoph Petz, Hans-Christian Hege, Kai Poethkow
WIND TUNNEL EXPERIMENTS ON PEDESTRIAN COMFORT AND VALIDATION OF CFD 'VIRTUAL WIND TUNNEL' MODEL
ICHMT DIGITAL LIBRARY ONLINE, Vol.13, 2008, issue
W. D. Wormgoor, G. M. van Uffelen
A MULTILEVEL APPROACH FOR SEQUENTIAL INFERENCE ON PARTIALLY OBSERVED DETERMINISTIC SYSTEMS
International Journal for Uncertainty Quantification, Vol.9, 2019, issue 4
Ajay Jasra, Yi Xu, Kody J.H. Law