Approximate Jacobian Eigenanalysis For Unstructured Mesh Optimization of Finite-Volume Simulations
Bibliographic record
Abstract
This paper presents a novel method for approximate eigenanalysis of large linear systems, with a specific focus on unstable eigenvalues in the Lyapunov sense. The method utilizes residual vector analysis, principal component analysis, and dynamic mode decomposition to identify unstable solution modes efficiently. Outlier detection models are employed to find the problematic cells on the unstructured mesh in the case of residual vector and principal component analysis while the dynamic mode decomposition points directly to the control volumes of interest without such help. By extracting and assembling corresponding rows of the Jacobian matrix, the large system is projected on a new matrix with significantly fewer degrees of freedom, leading to improved computational efficiency. The eigenvalue problem is then solved on this smaller matrix, and the obtained results are utilized for mesh optimization, enhancing the local stability of the dynamic system. By addressing the challenges of computational complexity and automation faced by previous methods, this novel approach offers a comprehensive and automated solution for the eigenanalysis of large linear systems. The potential impact of this method extends to various fields, providing a more efficient eigenanalysis process and opening new avenues for exploring and optimizing complex systems.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".