Data Compression Algorithms for Adjoint Based Sensitivity Studies of Unsteady Flows
Bibliographic record
Abstract
Adjoint based sensitivity studies are effective means to understand how flow quantities of interest and grid quality could affect the flow simulations. However, applying an unsteady adjoint method to three-dimensional complex flows remains a challenging topic. One of the challenges is that the flow variables at all previous time steps will be needed when solving the unsteady adjoint equation backwards in time. The straightforward treatment of storing all the previous flow solutions could be prohibitive for simulations with a large number of grid points and time steps. To avoid storing the full trajectory, the checkpointing method only stores the flow solutions at some carefully selected time steps called checkpoints, and re-computes the flow solutions between checkpoints when they are needed by the adjoint solver. However, the re-computation increases the computational cost by multiple times of the cost of solving the flow equations, which may be unacceptable for some applications. Alternatively, in this study, several data compression algorithms with much less extra cost were considered for alleviating the storage problem. In these data compression algorithms, the full flow solutions were projected onto a small set of bases which were either generated by the proper orthogonal decomposition (POD) method or by the Gram-Schmidt orthogonalization. Only a small set of bases and corresponding expansion coefficients need to be stored and they could recover the flow solutions at every time step with reasonable accuracy. The data compression algorithms were implemented in the numerical test cases, and the computed adjoint solutions were compared with that obtained by using full flow solutions. The comparisons demonstrated that the data compression algorithms were able to greatly reduce the storage requirements while maintaining sufficient accuracy.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".