Multifidelity Optimization Via Pattern Search and Space Mapping. Genetha Gray Computational Sciences & Mathematics Research Sandia National Labs, Livermore, CA.
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Computational Sciences & Mathematics Research
Sandia National Labs, Livermore, CA
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
Finite Element Mapping
Models of the
30,000 DOFMultifidelity Optimization (MFO)
Inherently (or embarrassingly) parallel,but processor load should be considered.
Note: Cannot Prune on Unsuccessful Iteration
We’re using the mappingSpace Mapping*: A Conduit Between the Low and High Fidelity Model Design Spaces
x – design variables
R - response
P - mapping
*Developed by John Bandler, et. al.
Oracle MappingThe MFO Scheme: Combining APPSPACK and Space Mapping
High Fidelity Mode
Low Fidelity Model
a (xH) b + g
A Simple Example Mapping
View of Unmapped Low Fidelity
View of High Fidelity Design Space
two calls to inner loop.
Approximate Inner Loop Call Locations within Hi-Fi Model
→ MFO high fidelity model
→ MFO low fidelity model
Objective Function Mapping
J(u) = installation costs + operation costs
Evaluation requires results of a simulation
Number of wells
Well pumping rates
Net pumping rate
Don’t flood or dry out land
No useless wells
Derivatives are unavailable
MODFLOW: used for flow equation (USGS)
MT3D: used for transport equation (EPA)Optimization
Initial cost: $78,586
MODFLOW (mf2k): ~2 seconds
mt3d: ~50 seconds
MFO development team (Sandia) Mapping
Joe Castro (PI), Electrical & Microsystem Modeling, NM
Tony Giunta, Validation & Uncertainty Quantification Processes, NM
Patty Hough, CSMR, CA
Katie Fowler, Clarkson University