An Integrated Approach to Parameter Learning in InfiniteDimensional Space
Abstract
The availability of sophisticated modern physics codes has greatly extended the ability of domain scientists to understand the processes underlying their observations of complicated processes, but it has also introduced the curse of dimensionality via the many userset parameters available to tune. Many of these parameters are naturally expressed as functional data, such as initial temperature distributions, equations of state, and controls. Thus, when attempting to find parameters that match observed data, being able to navigate parameterspace becomes highly nontrivial, especially considering that accurate simulations can be expensive both in terms of time and money. Existing solutions include batchparallel simulations, highdimensional, derivativefree optimization, and expert guessing, all of which make some contribution to solving the problem but do not completely resolve the issue. In this work, we explore the possibility of coupling together all three of the techniques just described by designing userguided, batchparallel optimization schemes. Our motivating example is a neutron diffusion partial differential equation where the timevarying multiplication factor serves as the unknown control parameter to be learned. We find that a simple, batchparallelizable, randomwalk scheme is able to make some progress on the problem but does not by itself produce satisfactory results. After reducing the dimensionality ofmore »
 Authors:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1392846
 Report Number(s):
 LAUR1728326
 DOE Contract Number:
 AC5206NA25396
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Boyd, Zachary M., and Wendelberger, Joanne Roth. An Integrated Approach to Parameter Learning in InfiniteDimensional Space. United States: N. p., 2017.
Web. doi:10.2172/1392846.
Boyd, Zachary M., & Wendelberger, Joanne Roth. An Integrated Approach to Parameter Learning in InfiniteDimensional Space. United States. doi:10.2172/1392846.
Boyd, Zachary M., and Wendelberger, Joanne Roth. 2017.
"An Integrated Approach to Parameter Learning in InfiniteDimensional Space". United States.
doi:10.2172/1392846. https://www.osti.gov/servlets/purl/1392846.
@article{osti_1392846,
title = {An Integrated Approach to Parameter Learning in InfiniteDimensional Space},
author = {Boyd, Zachary M. and Wendelberger, Joanne Roth},
abstractNote = {The availability of sophisticated modern physics codes has greatly extended the ability of domain scientists to understand the processes underlying their observations of complicated processes, but it has also introduced the curse of dimensionality via the many userset parameters available to tune. Many of these parameters are naturally expressed as functional data, such as initial temperature distributions, equations of state, and controls. Thus, when attempting to find parameters that match observed data, being able to navigate parameterspace becomes highly nontrivial, especially considering that accurate simulations can be expensive both in terms of time and money. Existing solutions include batchparallel simulations, highdimensional, derivativefree optimization, and expert guessing, all of which make some contribution to solving the problem but do not completely resolve the issue. In this work, we explore the possibility of coupling together all three of the techniques just described by designing userguided, batchparallel optimization schemes. Our motivating example is a neutron diffusion partial differential equation where the timevarying multiplication factor serves as the unknown control parameter to be learned. We find that a simple, batchparallelizable, randomwalk scheme is able to make some progress on the problem but does not by itself produce satisfactory results. After reducing the dimensionality of the problem using functional principal component analysis (fPCA), we are able to track the progress of the solver in a visually simple way as well as viewing the associated principle components. This allows a human to make reasonable guesses about which points in the state space the random walker should try next. Thus, by combining the random walker's ability to find descent directions with the human's understanding of the underlying physics, it is possible to use expensive simulations more efficiently and more quickly arrive at the desired parameter set.},
doi = {10.2172/1392846},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2017,
month = 9
}

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