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PHYSICS-BASED COVARIANCE MODELS FOR GAUSSIAN PROCESSES WITH MULTIPLE OUTPUTS
 

Summary: PHYSICS-BASED COVARIANCE MODELS FOR
GAUSSIAN PROCESSES WITH MULTIPLE OUTPUTS
Emil M Constantinescu
& Mihai Anitescu
Mathematics and Computer Science Division, Argonne National Laboratory, 9600 S. Cass Ave.,
Argonne, IL, 60439, USA
Original Manuscript Submitted: ; Final Draft Received:
Gaussian process analysis of processes with multiple outputs is limited by the fact that far fewer good classes of covari-
ance 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 pro-
cess. 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 co-kriging.
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 interrelate the output quantities). Our
results demonstrate the effectiveness of the approach on both synthetic and realistic data sets.
KEY WORDS: Gaussian random field; Spatial uncertainty; Model calibration; Spatial statistics

  

Source: Anitescu, Mihai - Mathematics and Computer Science Division, Argonne National Laboratory

 

Collections: Mathematics