Advances to modeling and solving infinite-dimensional optimization problems in InfiniteOpt.jl
Bibliographic record
Abstract
This paper details two extensions for the unifying abstraction behind InfiniteOpt.jl : infinite-dimensional generalized disjunctive programming (InfiniteGDP) and GPU-compatible direct transcription solution techniques with an abstraction called InfiniteSIMD-NLP. InfiniteOpt.jl is a Julia package that provides an efficient framework for formulating and solving a wide range of infinite-dimensional optimization (InfiniteOpt) problems. The InfiniteGDP abstraction builds upon traditional GDP techniques to enable intuitive modeling of discrete events and complex logic over continuous domains (e.g., position, time, and/or uncertainty); this abstraction is implemented in InfiniteDisjunctiveProgramming.jl . Moreover, the InfiniteSIMD-NLP abstraction, implemented in InfiniteExaModels.jl , exploits the recurrent structure of transcribed InfiniteOpt problems to efficiently discretize, differentiate, and solve such problems on high performance CPU and GPU architectures. We use a diverse set of case studies in dynamic, PDE-constrained, and stochastic optimization to demonstrate the relative merits of these abstraction extensions. The results demonstrate the utility of the InfiniteGDP abstraction to model continuous space–time switching constraints and how the InfiniteSIMD-NLP abstraction is able to accelerate the solution of InfiniteOpt problems by one to two orders-of-magnitude relative to existing state-of-the-art approaches.
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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 | 0.002 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".