Multi-Period Dynamic Optimization for Large-Scale Differential-Algebraic Process Models under Uncertainty
Bibliographic record
Abstract
A technique for optimizing large-scale differential-algebraic process models under uncertainty using a parallel embedded model approach is developed in this article. A combined multi-period multiple-shooting discretization scheme is proposed, which creates a significant number of independent numerical integration tasks for each shooting interval over all scenario/period realizations. Each independent integration task is able to be solved in parallel as part of the function evaluations within a gradient-based non-linear programming solver. The focus of this paper is on demonstrating potential computation performance improvement when the embedded differential-algebraic equation model solution of the multi-period discretization is implemented in parallel. We assess our parallel dynamic optimization approach on two case studies; the first is a benchmark literature problem, while the second is a large-scale air separation problem that considers a robust set-point transition under parametric uncertainty. Results indicate that focusing on the speed-up of the embedded model evaluation can significantly decrease the overall computation time; however, as the multi-period formulation grows with increased realizations, the computational burden quickly shifts to the internal computation performed within the non-linear programming algorithm. This highlights the need for further decomposition, structure exploitation and parallelization within the non-linear programming algorithm and is the subject for further investigation.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 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 | 0.000 |
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".