Solver-Free Data Generation for Training Neural Networks with Applications in Power Flow Analysis
Bibliographic record
Abstract
As universal function approximators, Neural Networks (NN) can approximate any function with less than a desired error anywhere within a bounded domain. However, existing studies that train NNs to solve optimization problems based on solver-generated datasets, cannot yet produce predictions with desired accuracy. Motivated by the Universal Approximation Theorem (UAT), this paper examines the accuracy of NN prediction in relation to dataset size, problem size, and the construction of training data. Our study shows that a sufficiently large NN can produce accurate predictions when trained with very large datasets, but even so its performance is limited by the quality of the training dataset, which is traditionally obtained by the solution of optimization problems for any given input. A novel data generation approach is proposed for training NN to solve optimization problems, particularly the power flow (PF) problem. The method bypasses the need for solvers to construct datasets by directly utilizing the PF equations. Applications to IEEE test systems show that the proposed approach outperforms solver-based NNs and different optimization algorithms by a wide margin.
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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 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".