Modeling of complex dynamic systems using differential neural networks with the incorporation of a priori knowledge
Bibliographic record
Abstract
In this paper, neural algorithms, including the multi-layered perceptron (MLP) differential approximator , generalized hybrid power series, discrete Hopfield neural network, and the hybrid numerical, are used for constructing models that incorporate a priori knowledge in the form of differential equations for dynamic engineering processes . The properties of these approaches are discussed and compared to each other in terms of efficiency and accuracy. The presented algorithms have a number of advantages over other traditional mesh-based methods such as reduction of the computational cost, speed up of the execution time , and data integration with the a priori knowledge . Furthermore, the presented techniques are applicable when the differential equations governing a system or dynamic engineering process are not fully understood. The proposed algorithms learn to compute the unknown or free parameters of the equation from observations of the process behavior , hence a more precise theoretical description of the process is obtained. Additionally, there will be no need to solve the differential equation each time the free parameters change. The parallel nature of the approaches outlined in this paper make them attractive for parallel implementation in dynamic engineering processes .
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| 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) | 0.001 | 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".