PRECISION GROWTH MODELING OF ESCHERICHIA COLI IN SPARSE DATA SCENARIOS: A MULTI-STAGE LEARNING APPROACH

Abstract

This study investigates the prediction of Escherichia coli growth in environments where experimental data are limited, by integrating mathematical curve fitting with machine learning regression models. Two hybrid frameworks are developed: Fourier Series Curve Fitting combined with Gaussian Process Regression (FSCF-GPR), and Gaussian Curve Fitting integrated with Support Vector Machine Regression (GCF-SVMR). The raw dataset, initially composed of only 10 experimental measurements, was expanded to 114 data points through mathematical smoothing, providing a richer basis for model training. Model performance was assessed using Root Mean Square Error (RMSE), Mean Squared Error (MSE), Coefficient of Determination (R²), and Mean Absolute Error (MAE). Results demonstrate that the FSCF-GPR framework achieved outstanding predictive accuracy with an R² of 0.9999, while GCF-SVMR also showed strong performance with an R² of 0.9934. These findings highlight that data augmentation via curve fitting can substantially enhance the accuracy and robustness of machine learning approaches in microbiological growth prediction under data-scarce conditions.

Keywords

• Microbial growth modeling
• Data augmentation
• Machine learning
• Regression model

Ethical Statement

No conflict of interest was declared by the authors.

SEYREK VERİ SENARYOLARINDA ESCHERICHIA COLI'NİN HASSAS BÜYÜME MODELLEMESİ: ÇOK AŞAMALI BİR ÖĞRENME YAKLAŞIMI

Abstract

Bu çalışma, matematiksel eğri uydurma ile makine öğrenimi regresyon modellerini entegre ederek, deneysel verilerin sınırlı olduğu ortamlarda Escherichia coli büyümesinin tahminini araştırmaktadır. İki hibrit çerçeve geliştirilmiştir: Gauss Süreci Regresyonu ile birleştirilmiş Fourier Serisi Eğri Uydurma (FSCF-GPR) ve Destek Vektör Makinesi Regresyonu ile entegre edilmiş Gauss Eğri Uydurma (GCF-SVMR). Başlangıçta sadece 10 deneysel ölçümden oluşan ham veri kümesi, matematiksel düzeltme yoluyla 114 veri noktasına genişletilerek model eğitimi için daha zengin bir temel sağlanmıştır. Model performansı, Kök Ortalama Kare Hatası (RMSE), Ortalama Kare Hatası (MSE), Belirleme Katsayısı (R²) ve Ortalama Mutlak Hata (MAE) kullanılarak değerlendirilmiştir. Sonuçlar, FSCF-GPR çerçevesinin 0,9999 R² ile olağanüstü bir tahmin doğruluğu elde ettiğini, GCF-SVMR'nin ise 0,9934 R² ile güçlü bir performans gösterdiğini ortaya koymaktadır. Bu bulgular, eğri uydurma yoluyla veri artırmanın, veri kıtlığı koşullarında mikrobiyolojik büyüme tahmininde makine öğrenimi yaklaşımlarının doğruluğunu ve sağlamlığını önemli ölçüde artırabileceğini vurgulamaktadır.

Keywords

• Mikrobiyal büyüme modellemesi
• Veri artırma
• Makine öğrenmesi
• Regresyon model

References

1. References
2. Baranyi, J., Roberts, T. A., 1994. A dynamic approach to predicting bacterial growth in food. International Journal of Food Microbiology, 23, 277--294.
3. Berwald, J., Gedeon, T., Sheppard, J., 2012Using machine learning to predict catastrophes in dynamical systems, J. Comput. Appl. Math. 236(9), 2235-2245.
4. Cheroutre-Vialette, M. , Lebert, A., 2002. Application of recurrent neural network to predict bacterial growth in dynamic conditions, International Journal of Food Microbiology, 73, 107-118.
5. Di Sciascio, F., Amicarelli, A.N., 2008. Biomass estimation in batch biotechnological processes by Bayesian Gaussian process regression, Computers & Chemical Engineering, 32, 3264--327.
6. Fujikawa, H., Kai, A., Morozumi, S., 2004. A new logistic model for Escherichia coli growth at constant and dynamic temperatures, Food Microbiology, 21, 501-509.
7. Geeraerd, A.H., Herremans, C.H., Van Impe, J.F., 2000. Structural model requirements to describe microbial inactivation during a mild heat treatment, International Journal of Food Microbiology, 59 185-209.
8. Jeyamkondan, S., Jayas, D.S., Holley, R.A., 2001.Microbial growth modelling with artificial neural networks. International Journal of Food Microbiology, 64 343-354.

9. Shamsudin, S.N., Rahiman, M.H.F., Taib, M.N, Ahmad, A.H, Razak, R.W.A., 2017 Escherichia coli growth modeling using neural network. J. Fundam. Appl. Sci., 9, 759-771.
10. Al, S., Uysal Ciloglu, F., Akcay, A., Koluman, A., 2024. Machine learning models for prediction of Escherichia coli O157: H7 growth in raw ground beef at different storage temperatures, Meat Science, 210, 1-7.
11. Chitra, M., Sutha, S., Pappa, N., 2021. Application of deep neural techniques in predictive modelling for the estimation of Escherichia coli growth rate, Journal of Applied Microbiology, 130(5), 1645-1655.
12. Rizki, W. M., Ratih D. H, Harsi D.K, 2022. Comparison of Predictive Growth Models for Bacillus Cereus in Cooked and Fried Rice During Storage, The Annals of the University Dunarea De Jos of Galati. Fascicle VI - Food Technology, 46 (2), 89-103.
13. Juneja, V.K., Golden, C. E., Mishra, A., Harrison, M., Mohr T.B., 2019. Predictive model for growth of Bacillus cereus at temperatures applicable to cooling of cooked pasta, Journal of Food Science , 84(3), 590-598.
14. Choi, M.S., Kim, J.Y., Jeon, E.B., Park, S.Y., 2020. Predictive growth models of Bacillus cereus on dried laver Pyropia pseudolinearis as a function of storage temperature. Korean Journal of Fisheries and Aquatic Sciences, 53(5), 699-706.
15. Jiang, Y.N., Luo, J., Huang, D., Liu, Y., Li, D., 2022. Machine learning advances in microbiology: A review of methods and applications. Frontiers in Microbiology, 13, Article 925454.
16. Weller, D., Love, T., Wiedmann M., (2021). Interpretability versus accuracy: A comparison of machine learning models built using different algorithms, performance measures, and features to predict E. coli levels in agricultural water, Frontiers in Artificial Intelligence, 4, Article 628441.
17. Ince, V., Bader-El-Den, M., Arabikhan, F., Sari, O. F., 2024. Machine Learning for Bacterial Growth Prediction and Examination of Bacterial Impact on Growth, In 2024 IEEE 12th International Conference on Intelligent Systems (IS), 1-6.
18. Kowalik, J., Lobacz, A., Zulewska, J., Dec, B., 2018. Analysis and mathematical modelling of the behaviour of Escherichia coli in the mascarpone cheese during cold storage. International Journal of Food Science and Technology, 53(6), 1541–1548.
19. Martinez-Rios, V., Gkogka, E., Dalgaard, P., 2020. Predicting growth of Listeria monocytogenes at dynamic conditions during manufacturing, ripening and storage of cheese - Evaluation and application of models. Food Microbiology, 92, 1–12.
20. Palar, P.S., Zakaria, K, Zuhal, L.R., Shimoyama, K., Liem, R.P., 2021. Gaussian processes and support vector regression for uncertainty quantification in aerodynamics. AIAA Scitech 2021 Forum ( AIAA, 2021), p. 0181.
21. Stavropoulou, E. and Bezirtzoglou, E., 2019. Predictive modeling of microbial behavior in food. Foods, 8(12) 1-16.
22. Baranyi, J., Buss da Silva, N., and Ellouze, M., 2017. Rethinking tertiary models: relationships between growth parameters of Bacillus cereus strains. Front. Food Microbiol., 8, 1-8.