CAM colloquium - Friday, February 17
3:30 p.m.
655 Rhodes Hall
Speaker: Christine Shoemaker, School of Civil and Environmental
Engineering and School of Operations Research and Industrial Engineering,
Cornell
Title: “Function Approximation Algorithms for Continuous Optimization
of
Multi-modal Computationally Expensive Models with Applications
Abstract: Many important problems in engineering and science
require optimization of a computationally expensive (costly) function.
These applications include calibration of model parameters to data
and/or optimizing a design or operational plan to met an economic
objective. With computationally expensive functions (like nonlinear
systems of partial differential equations), this optimization is made
difficult by the limited number of model simulations that can be done
because each simulation takes a long time (e.g. an hour or more).
The optimization problem is even more difficult if it has multiple
local optima, thereby requiring a global optimization algorithm.
Our new algorithms use function approximation methods and experimental
design to approximate the objective function based on previous costly
function evaluations. Function approximation is combined with locations
of previous costly function evaluations to select iteratively the
next costly function evaluation. The theorem for convergence to the
global minimum will be described.
Numerical algorithm comparisons will be presented for test functions
and for an environmentally based partial differential equation model
that requires 3 hours to run for each simulation. This nonlinear model
(based on fluid mechanics and chemical reactions) describes the transport
of water and pollutants in a groundwater aquifer. The optimization
is used for calibration of the model by selecting the parameter values
(decision variables) that best fit measured data. The parameter surface
is multi-modal so this is a global optimization problem. The results
indicate that the Regis and Shoemaker method generally gives better
results for global optimization test problems and the environmental
model than alternative methods when the number of model simulations
is limited.
I will also discuss briefly a new joint NSF project on using our
function approximation optimization methods in the context of Bayesian
analysis of uncertainty. In this project we are combining optimization
for calibration with an assessment of the uncertainty in calibrated
parameter estimates and in calibrated model output based on input
data.
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All this work has been done jointly with Rommel Regis. Parts of the
seminar will discuss work done with Pradeep Mugunthan, David Ruppert,
and Nikolai Blizniouk
Prof. Shoemaker will probably offer a special CIS M.S./Ph.D.
course in fall 2006 on local and global optimization using function
approximation with applications to computationally expensive functions
for design optimization, calibration, and uncertainty assessment.
Interested students are encouraged to contact Prof. Shoemaker.
Refreshments at 4:30 in 657 Rhodes Hall.