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Title: Efficient checkpointing schemes for depletion perturbation solutions on memory-limited architectures

Abstract

We describe a methodology for decreasing the memory footprint and machine I/O load associated with the need to access a forward solution during an adjoint solve. Specifically, we are interested in the depletion perturbation equations, where terms in the adjoint Bateman and transport equations depend on the forward flux solution. Checkpointing is the procedure of storing snapshots of the forward solution to disk and using these snapshots to recompute the parts of the forward solution that are necessary for the adjoint solve. For large problems, however, the storage cost of just a few copies of an angular flux vector can exceed the available RAM on the host machine. We propose a methodology that does not checkpoint the angular flux vector; instead, we write and store converged source moments, which are typically of a much lower dimension than the angular flux solution. This reduces the memory footprint and I/O load of the problem, but requires that we perform single sweeps to reconstruct flux vectors on demand. We argue that this trade-off is exactly the kind of algorithm that will scale on advanced, memory-limited architectures. We analyze the cost, in terms of FLOPS and memory footprint, of five checkpointing schemes. We alsomore » provide computational results that support the analysis and show that the memory-for-work trade off does improve time to solution. (authors)« less

Authors:
; ;  [1]
  1. Texas A and M University, Department of Nuclear Engineering, 3133 TAMU, College Station, TX 77843-3133 (United States)
Publication Date:
Research Org.:
American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL 60526 (United States)
OSTI Identifier:
22212892
Resource Type:
Conference
Resource Relation:
Conference: M and C 2013: 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Sun Valley, ID (United States), 5-9 May 2013; Other Information: Country of input: France; 17 refs.; Related Information: In: Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - M and C 2013| 3016 p.
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; EQUATIONS; MATHEMATICAL SOLUTIONS; PERTURBATION THEORY; TRANSPORT THEORY; VECTORS

Citation Formats

Stripling, H. F., Adams, M. L., and Hawkins, W. D. Efficient checkpointing schemes for depletion perturbation solutions on memory-limited architectures. United States: N. p., 2013. Web.
Stripling, H. F., Adams, M. L., & Hawkins, W. D. Efficient checkpointing schemes for depletion perturbation solutions on memory-limited architectures. United States.
Stripling, H. F., Adams, M. L., and Hawkins, W. D. 2013. "Efficient checkpointing schemes for depletion perturbation solutions on memory-limited architectures". United States.
@article{osti_22212892,
title = {Efficient checkpointing schemes for depletion perturbation solutions on memory-limited architectures},
author = {Stripling, H. F. and Adams, M. L. and Hawkins, W. D.},
abstractNote = {We describe a methodology for decreasing the memory footprint and machine I/O load associated with the need to access a forward solution during an adjoint solve. Specifically, we are interested in the depletion perturbation equations, where terms in the adjoint Bateman and transport equations depend on the forward flux solution. Checkpointing is the procedure of storing snapshots of the forward solution to disk and using these snapshots to recompute the parts of the forward solution that are necessary for the adjoint solve. For large problems, however, the storage cost of just a few copies of an angular flux vector can exceed the available RAM on the host machine. We propose a methodology that does not checkpoint the angular flux vector; instead, we write and store converged source moments, which are typically of a much lower dimension than the angular flux solution. This reduces the memory footprint and I/O load of the problem, but requires that we perform single sweeps to reconstruct flux vectors on demand. We argue that this trade-off is exactly the kind of algorithm that will scale on advanced, memory-limited architectures. We analyze the cost, in terms of FLOPS and memory footprint, of five checkpointing schemes. We also provide computational results that support the analysis and show that the memory-for-work trade off does improve time to solution. (authors)},
doi = {},
url = {https://www.osti.gov/biblio/22212892}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Jul 01 00:00:00 EDT 2013},
month = {Mon Jul 01 00:00:00 EDT 2013}
}

Conference:
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