Sensitivity analysis of chaotic dynamical systems using a physics-constrained data-driven approach
Bibliographic record
Abstract
This study proposes a new physics-constrained data-driven approach for sensitivity analysis and uncertainty quantification of large-scale chaotic Partial Differential Equations (PDEs). Unlike conventional sensitivity analysis, the proposed approach can manipulate the unsteady sensitivity function (i.e., tangent) for PDE-constrained optimizations. In this new approach, high-dimensional governing equations from physical space are transformed into an unphysical space (i.e., Hilbert space) to develop a closure model in the form of a Reduced-Order Model (ROM). This closure model is derived explicitly from the governing equations to set strong constraints on manifolds in Hilbert space. Afterward, a new data sampling method is proposed to build a data-driven approach for this framework. A series of least squares minimizations are set in the form of a novel auto-encoder system to solve this closure model. To compute sensitivities, least-squares shadowing minimization is applied to the ROM. It is shown that the proposed approach can capture sensitivities for large-scale chaotic dynamical systems, where finite difference approximations fail.
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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 | 0.001 |
| 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 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".