Optimization of Neural Network architecture and derivation of closed-form equation to predict ultimate load of functionally graded material plate
Bibliographic record
Abstract
Functionally Graded Material (FGM) plate is a complicated structure with complex allocation of spatially changing proportions of ceramic and metal within the matter. Various analytical and numerical methods have been applied with a view to evaluating the critical load of FGM plate. However, these conventional methods struggle when the computational complexity is significant, which represents an obstacle to incorporation with other advanced techniques where computational power is required (e.g. optimization or random simulations). The Neural Network (NNet) model has been successfully applied to resolve this issue. However, the conventional NNet requires proper configuration to take advantage of the model, and thus, careful parameter tuning is required. Furthermore, the NNet is typically a "black box," where the prediction mechanism is hidden. This paper establishes an optimized architecture for NNet, with parametric study of the model's hyperparameters. Variance propagation is also applied to observe the variation of the model's performance on random sub-databases splintered from the database. To this end, the explicit expression of the trained NNet model is provided after mathematically deploying the hidden algebra behind an NNet prediction. The developed model has very promising evaluation metrics: R 2 , MAE, and RMSE on the test set are 0.999925, 0.067516, and 0.146438, respectively.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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".