A Numerical DAE Approach for Solving a System Dynamics Problem
Bibliographic record
Abstract
A system dynamics model first developed using the software STELLA, which explores the complex behaviour of the financially sustainable management of wastewater distribution infrastructure, was converted here into a system of coupled non-linear differential algebraic equations (DAEs). Each differential equation involved a time derivative on a primary variable specifying the temporal evolution of the system. In addition, algebraic (secondary) equations and variables specified the non-linearity inherent in the system as well as any controls on the primary variables constraining the physical evolution of the system relevant to the problem at hand. While STELLA employed a Runge-Kutta numerical strategy, the numerical DAE method used a fully-explicit scheme combined with a fixed-point iteration to resolve the non-linearity. The Runge-Kutta and numerical DAE solutions deviate markedly when the non-linearity of the system becomes pronounced. We demonstrate point-wise stability of the numerical DAE solution as the timestep is refined.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".