Innovative mathematical correlations for estimating mono-nanofluids' density: Insights from white-box machine learning
Why this work is in the frame
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Bibliographic record
Abstract
• The current study proposes innovative mathematical correlations for estimating the density of mono-nanofluids. • An extensive and comprehensive data bank comprising 4004 experimental data-points was employed to guarantee the robustness and applicability of the derived correlations. • Two rigorous machine-learning techniques, namely Group Method of Data Handling (GMDH) and Gene Expression Programming (GEP), were used to develop correlations. • The GEP-based correlation was highlighted as the most accurate model, with AAPRE=0.6614% and R 2 =0.9671. • The key findings and implications of this study can significantly advance the applied fields of thermal engineering. The current research offers credible mathematical models solely for estimating mono-nanofluids' density ( ρ nf ), which can be useful for thermal engineering calculations required by various industries and applications. Accordingly, a comprehensive data bank encompassing 4004 experimental data-points was utilized to execute two rigorous machine-learning techniques: Group Method of Data Handling (GMDH) and Gene Expression Programming (GEP). Subsequently, two high-accuracy correlations were fine-tuned based on the four independent variables: average nanoparticle diameter ( d np ), nanoparticle mass concentration ( ϕ m ), nanoparticle density ( ρ np ), and base-fluid density ( ρ bf ). Two variables pressure ( P ) and temperature ( T ), with rather minor impacts on the density of the mono-nanofluids under investigation, were excluded in the final correlations as a result of the modeling process and the intelligent operation of the machine-learning techniques. By performing multiple statistical and graphical analyses, comparative evaluations highlighted the superior performance and outstanding accuracy of the GEP-based correlation (with AAPRE=0.6614% and R 2 =0.9671). Moreover, sensitivity analysis and parametric trend assessments revealed that ϕ m and ρ bf were the most crucial variables affecting ρ nf values, with relevancy factors of approximately 0.72 and 0.71, respectively. By considering the GEP-based correlation's outputs and applying the leverage statistical approach, a considerable portion (96.33%) of the total data-points was identified as valid data.
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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 it