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|
Mohit Kumar
| Speaker: |
Mohit Kumar (TU/e)
|
| Date: |
Wednesday July 6, 2011
|
| Title: |
Optimization
of Scaling Parameter in Kriging and Polyharmonic
Approximation Methods (Master's thesis
presentation)
|
Abstract
|
|
Yieldstar
is
a meteorological tool developed by ASML, for the purpose of
validating the lithographic process, i.e., to check if the integrated
circuits (ICs) are fabricated according to (height, width, etc.) the
desired specifications. This thesis first examines the construction of
an approximation model of a multi-variable function. The multi-variable
function is related to the inverse of a Maxwell operator, the variables
are typically material constants and geometric parameters. Yieldstar
currently employs Kriging model as a computationally inexpensive
approximation of computationally expensive discrete Maxwell solver. In
this thesis, we provide with a new method called Polyharmonic method to
make approximation model. In the study we find that Polyharmonic
model gives better results than Kriging model in terms of prediction
accuracy. Both approximation models contain a scaling parameter which
controls the prediction accuracy of the model. Due to non-availability
of derivative information, derivative free optimization methods are
first examined to calculate the optimal value of scaling parameter. To
make the optimization process fast, the problem of parameter
optimization is then transformed into the problem of parameter
estimation using Maximum Likelihood Estimation (MLE). The transformed
problem gives results much faster than all examined derivative free
methods and brute force method used by ASML. |
|
