Towards efficient backward-in-time adjoint computations using data compression techniques
Abstract
In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, the state-of-the-practice is to use adjoint approaches which require the solution of a backward-in-time problem defined by a linearization of the forward problem. One of the major obstacles in the practical application of these approaches, we found, is the need to store, or recompute, the forward solution to define the adjoint problem and to evaluate the error representation. Our study considers the use of data compression techniques to approximate forward solutions employed in the backward-in-time integration. The development derives an error representation that accounts for the difference between the standard-approach and the compressed approximation of the forward solution. This representation is algorithmically similar to the standard representation and only requires the computation of the quantity of interest for the forward solution and the data-compressed reconstructed solution (i.e. scalar quantities that can be evaluated as the forward problem is integrated). This approach is then compared with existing techniques, such as checkpointing and time-averaged adjoints. Lastly, we provide numerical results indicating the potential efficiency of our approach on a transient diffusion–reaction equation and on the Navier–Stokes equations. These results demonstrate memory compression ratios up to 450×450× while maintainingmore »
- Authors:
-
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1141564
- Report Number(s):
- SAND-2014-2541J
Journal ID: ISSN 0045-7825; PII: S0045782514004800
- Grant/Contract Number:
- AC04-94AL85000
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Methods in Applied Mechanics and Engineering
- Additional Journal Information:
- Journal Volume: 288; Journal Issue: C; Journal ID: ISSN 0045-7825
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; data compression; adjoint problem; error analysis; navier-stokes
Citation Formats
Cyr, E. C., Shadid, J. N., and Wildey, T. Towards efficient backward-in-time adjoint computations using data compression techniques. United States: N. p., 2014.
Web. doi:10.1016/j.cma.2014.12.001.
Cyr, E. C., Shadid, J. N., & Wildey, T. Towards efficient backward-in-time adjoint computations using data compression techniques. United States. https://doi.org/10.1016/j.cma.2014.12.001
Cyr, E. C., Shadid, J. N., and Wildey, T. Tue .
"Towards efficient backward-in-time adjoint computations using data compression techniques". United States. https://doi.org/10.1016/j.cma.2014.12.001. https://www.osti.gov/servlets/purl/1141564.
@article{osti_1141564,
title = {Towards efficient backward-in-time adjoint computations using data compression techniques},
author = {Cyr, E. C. and Shadid, J. N. and Wildey, T.},
abstractNote = {In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, the state-of-the-practice is to use adjoint approaches which require the solution of a backward-in-time problem defined by a linearization of the forward problem. One of the major obstacles in the practical application of these approaches, we found, is the need to store, or recompute, the forward solution to define the adjoint problem and to evaluate the error representation. Our study considers the use of data compression techniques to approximate forward solutions employed in the backward-in-time integration. The development derives an error representation that accounts for the difference between the standard-approach and the compressed approximation of the forward solution. This representation is algorithmically similar to the standard representation and only requires the computation of the quantity of interest for the forward solution and the data-compressed reconstructed solution (i.e. scalar quantities that can be evaluated as the forward problem is integrated). This approach is then compared with existing techniques, such as checkpointing and time-averaged adjoints. Lastly, we provide numerical results indicating the potential efficiency of our approach on a transient diffusion–reaction equation and on the Navier–Stokes equations. These results demonstrate memory compression ratios up to 450×450× while maintaining reasonable accuracy in the error-estimates.},
doi = {10.1016/j.cma.2014.12.001},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 288,
place = {United States},
year = {Tue Dec 16 00:00:00 EST 2014},
month = {Tue Dec 16 00:00:00 EST 2014}
}
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Works referencing / citing this record:
Compression Challenges in Large Scale Partial Differential Equation Solvers
journal, September 2019
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- Algorithms, Vol. 12, Issue 9