3 research outputs found
Robust Experimental Designs for Model Calibration
A computer model can be used for predicting an output only after specifying
the values of some unknown physical constants known as calibration parameters.
The unknown calibration parameters can be estimated from real data by
conducting physical experiments. This paper presents an approach to optimally
design such a physical experiment. The problem of optimally designing physical
experiment, using a computer model, is similar to the problem of finding
optimal design for fitting nonlinear models. However, the problem is more
challenging than the existing work on nonlinear optimal design because of the
possibility of model discrepancy, that is, the computer model may not be an
accurate representation of the true underlying model. Therefore, we propose an
optimal design approach that is robust to potential model discrepancies. We
show that our designs are better than the commonly used physical experimental
designs that do not make use of the information contained in the computer model
and other nonlinear optimal designs that ignore potential model discrepancies.
We illustrate our approach using a toy example and a real example from
industry.Comment: 25 pages, 10 figure
Prediction in regression models with continuous observations
We consider the problem of predicting values of a random process or field
satisfying a linear model , where
errors are correlated. This is a common problem in kriging,
where the case of discrete observations is standard. By focussing on the case
of continuous observations, we derive expressions for the best linear unbiased
predictors and their mean squared error. Our results are also applicable in the
case where the derivatives of the process are available, and either a
response or one of its derivatives need to be predicted. The theoretical
results are illustrated by several examples in particular for the popular
Mat\'{e}rn kernel
Multivariate Rational Approximation
We present two approaches for computing rational approximations to
multivariate functions, motivated by their effectiveness as surrogate models
for high-energy physics (HEP) applications. Our first approach builds on the
Stieltjes process to efficiently and robustly compute the coefficients of the
rational approximation. Our second approach is based on an optimization
formulation that allows us to include structural constraints on the rational
approximation, resulting in a semi-infinite optimization problem that we solve
using an outer approximation approach. We present results for synthetic and
real-life HEP data, and we compare the approximation quality of our approaches
with that of traditional polynomial approximations