Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation
Adjoint equations of differential equations have seen widespread applications in optimization, inverse problems, and uncertainty quantification. A major challenge in solving adjoint equations for time dependent systems has been the need to use the solution of the original system in the adjoint calcu...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2011
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| Online Access: | http://hdl.handle.net/1721.1/67013 https://orcid.org/0000-0001-9669-2563 |
| _version_ | 1811085701084610560 |
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| author | Wang, Qiqi Moin, Parviz Iaccarino, Gianluca |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Wang, Qiqi Moin, Parviz Iaccarino, Gianluca |
| author_sort | Wang, Qiqi |
| collection | MIT |
| description | Adjoint equations of differential equations have seen widespread applications in optimization, inverse problems, and uncertainty quantification. A major challenge in solving adjoint equations for time dependent systems has been the need to use the solution of the original system in the adjoint calculation and the associated memory requirement. In applications where storing the entire solution history is impractical, checkpointing methods have frequently been used. However, traditional checkpointing algorithms such as revolve require a priori knowledge of the number of time steps, making these methods incompatible with adaptive time stepping. We propose a dynamic checkpointing algorithm applicable when the number of time steps is a priori unknown. Our algorithm maintains a specified number of checkpoints on the fly as time integration proceeds for an arbitrary number of time steps. The resulting checkpoints at any snapshot during the time integration have the optimal repetition number. The efficiency of our algorithm is demonstrated both analytically and experimentally in solving adjoint equations. This algorithm also has significant advantage in automatic differentiation when the length of execution is variable. |
| first_indexed | 2024-09-23T13:14:12Z |
| format | Article |
| id | mit-1721.1/67013 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:14:12Z |
| publishDate | 2011 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/670132022-10-01T13:54:01Z Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation Wang, Qiqi Moin, Parviz Iaccarino, Gianluca Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Wang, Qiqi Wang, Qiqi Adjoint equations of differential equations have seen widespread applications in optimization, inverse problems, and uncertainty quantification. A major challenge in solving adjoint equations for time dependent systems has been the need to use the solution of the original system in the adjoint calculation and the associated memory requirement. In applications where storing the entire solution history is impractical, checkpointing methods have frequently been used. However, traditional checkpointing algorithms such as revolve require a priori knowledge of the number of time steps, making these methods incompatible with adaptive time stepping. We propose a dynamic checkpointing algorithm applicable when the number of time steps is a priori unknown. Our algorithm maintains a specified number of checkpoints on the fly as time integration proceeds for an arbitrary number of time steps. The resulting checkpoints at any snapshot during the time integration have the optimal repetition number. The efficiency of our algorithm is demonstrated both analytically and experimentally in solving adjoint equations. This algorithm also has significant advantage in automatic differentiation when the length of execution is variable. United States. Dept. of Energy (Advanced Simulation and Computing (ASC) Program) Stanford University (Predictive Science Academic Alliance Program) 2011-11-14T18:06:26Z 2011-11-14T18:06:26Z 2009-06 2009-02 Article http://purl.org/eprint/type/JournalArticle 1064-8275 1095-7197 http://hdl.handle.net/1721.1/67013 Wang, Qiqi, Parviz Moin, and Gianluca Iaccarino. “Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation.” SIAM Journal on Scientific Computing 31 (2009): 2549. © 2009 Society for Industrial and Applied Mathematics. https://orcid.org/0000-0001-9669-2563 en_US http://dx.doi.org/10.1137/080727890 SIAM Journal on Scientific Computing Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics SIAM |
| spellingShingle | Wang, Qiqi Moin, Parviz Iaccarino, Gianluca Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation |
| title | Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation |
| title_full | Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation |
| title_fullStr | Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation |
| title_full_unstemmed | Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation |
| title_short | Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation |
| title_sort | minimal repetition dynamic checkpointing algorithm for unsteady adjoint calculation |
| url | http://hdl.handle.net/1721.1/67013 https://orcid.org/0000-0001-9669-2563 |
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