A Data-Driven Symbolic Regression Framework for Modeling and Multiobjective Optimization of a Microbial Fermentation System
Bibliographic record
Abstract
Effective control of bioprocess systems requires a deep understanding of the fundamental equations governing them. However, in a data-driven framework, the discovery of such guiding rules is hampered by noisy data and intricate nonlinear dynamics. This paper presents a data-driven symbolic regression (SR) approach to enhance the modeling of microbial fermentation systems for bioprocessing. Unlike traditional machine learning (ML) models that fit data to predefined structures, SR discovers both the model structure and the parameters, offering interpretable mathematical expressions. To this extent, in this study, dissolved oxygen, aeration, agitation, temperature, and pH were utilized to develop a symbolic expression with the cell biomass and protein concentration. Results demonstrated that SR models achieved better performance with higher R -square and lower root-mean-square error and mean absolute error than various baseline ML models. A multiobjective optimization technique, namely, nondominated sorting genetic algorithm-II (NSGA-II), was employed over the developed model to optimize cell biomass, protein concentration, and batch time. Further, the optimal results obtained by NSGA-II were experimentally verified through three sequential runs, yielding a mean percentage deviation of 4.50% and 3.26% for cell biomass and protein concentration, respectively. Overall, the results indicate that SR modeling offers a powerful, interpretable, and data-driven method for optimizing complex bioprocesses, outperforming conventional ML models in both understanding and enhancing microbial fermentation systems.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| 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 | 0.001 |
| 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".