{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T19:19:33Z","timestamp":1769023173169,"version":"3.49.0"},"reference-count":23,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T00:00:00Z","timestamp":1759276800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Algorithms"],"abstract":"<jats:p>This research introduces a hybrid framework that integrates stochastic modeling and machine learning for predicting postprandial glucose levels in individuals with Type 1 Diabetes (T1D). The primary aim is to enhance the accuracy of glucose predictions by merging a biophysical Glucose\u2013Insulin\u2013Meal (GIM) model with advanced machine learning techniques. This framework is tailored to utilize the Kaggle BRIST1D dataset, which comprises real-world data from continuous glucose monitoring (CGM), insulin administration, and meal intake records. The methodology employs the GIM model as a physiological prior to generate simulated glucose and insulin trajectories, which are then utilized as input features for the machine learning (ML) component. For this component, the study leverages the Light Gradient Boosting Machine (LightGBM) due to its efficiency and strong performance with tabular data, while Long Short-Term Memory (LSTM) networks are applied to capture temporal dependencies. Additionally, Bayesian regression is integrated to assess prediction uncertainty. A key advancement of this research is the transition from a deterministic GIM formulation to a stochastic differential equation (SDE) framework, which allows the model to represent the probabilistic range of physiological responses and improves uncertainty management when working with real-world data. The findings reveal that this hybrid methodology enhances both the precision and applicability of glucose predictions by integrating the physiological insights of Glucose Interaction Models (GIM) with the flexibility of data-driven machine learning techniques to accommodate real-world variability. This innovative framework facilitates the creation of robust, transparent, and personalized decision-support systems aimed at improving diabetes management.<\/jats:p>","DOI":"10.3390\/a18100623","type":"journal-article","created":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T15:20:38Z","timestamp":1759332038000},"page":"623","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Hybrid Stochastic\u2013Machine Learning Framework for Postprandial Glucose Prediction in Type 1 Diabetes"],"prefix":"10.3390","volume":"18","author":[{"given":"Irina","family":"Naskinova","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, 1 Hristo Smirnenski Blvd., 1164 Sofia, Bulgaria"}]},{"given":"Mikhail","family":"Kolev","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, 1 Hristo Smirnenski Blvd., 1164 Sofia, Bulgaria"},{"name":"Faculty of Fire Safety and Civil Protection, Academy of the Ministry of Interior, 170 Pirotska Str., 1309 Sofia, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-9577-654X","authenticated-orcid":false,"given":"Dilyana","family":"Karova","sequence":"additional","affiliation":[{"name":"Department of Statistics and Econometrics, Faculty of Economics and Business Administration, Sofia University \u2018St. Kliment Ohridski\u2019, 125 Tsarigradsko Shosse Blvd., bl. 3, 1113 Sofia, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1756-3358","authenticated-orcid":false,"given":"Mariyan","family":"Milev","sequence":"additional","affiliation":[{"name":"Department of Statistics and Econometrics, Faculty of Economics and Business Administration, Sofia University \u2018St. Kliment Ohridski\u2019, 125 Tsarigradsko Shosse Blvd., bl. 3, 1113 Sofia, Bulgaria"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"98","DOI":"10.34172\/hpp.2020.18","article-title":"Prevalence and incidence of type 1 diabetes in the world: A systematic review and meta-analysis","volume":"10","author":"Mobasseri","year":"2020","journal-title":"Health Promot. Perspect."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1007\/s00125-018-4763-3","article-title":"Trends and cyclical variation in the incidence of childhood type 1 diabetes in 26 european centers in the 25-year period 1989\u20132013","volume":"62","author":"Patterson","year":"2019","journal-title":"Diabetologia"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"109119","DOI":"10.1016\/j.diabres.2021.109119","article-title":"IDF diabetes atlas: Global, regional and country-level diabetes prevalence estimates for 2021 and projections for 2045","volume":"183","author":"Sun","year":"2022","journal-title":"Diabetes Res. Clin. Pract."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2337\/diabetes.54.1.1","article-title":"Postprandial hyperglycemia and diabetes complications: Is it time to treat?","volume":"54","author":"Ceriello","year":"2005","journal-title":"Diabetes"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1111\/j.1464-5491.2008.02565.x","article-title":"International diabetes federation guideline for management of postmeal glucose: A review of recommendations","volume":"25","author":"Ceriello","year":"2008","journal-title":"Diabet. Med."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"881","DOI":"10.2337\/diacare.26.3.881","article-title":"Contributions of fasting and postprandial plasma glucose increments to the overall diurnal hyperglycemia of type 2 diabetic patients: Variations with increasing levels of hba1c","volume":"26","author":"Monnier","year":"2003","journal-title":"Diabetes Care"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1740","DOI":"10.1109\/TBME.2007.893506","article-title":"Meal simulation model of the glucose\u2013insulin system","volume":"54","author":"Rizza","year":"2007","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1109\/10.740875","article-title":"Glucose effectiveness and insulin sensitivity from the minimal models","volume":"46","author":"Vicini","year":"1999","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1088\/0967-3334\/25\/4\/010","article-title":"Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes","volume":"25","author":"Hovorka","year":"2004","journal-title":"Physiol. Meas."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0025-5564(82)90050-5","article-title":"An integrated mathematical model of the dynamics of blood glucose and its hormonal control","volume":"58","author":"Cobelli","year":"1982","journal-title":"Math. Biosci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1080\/00207160.2022.2142041","article-title":"Novel methodological and computational techniques for uncertainty quantification in diabetes short-term management models using real data","volume":"101","author":"Hidalgo","year":"2024","journal-title":"Int. J. Comput. Math."},{"key":"ref_12","unstructured":"Sorensen, J.T. (1985). A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes. [PhD Thesis, Massachusetts Institute of Technology]."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1177\/193229681300700220","article-title":"Model identification using stochastic differential equation grey-box models in diabetes","volume":"7","author":"Schmidt","year":"2013","journal-title":"J. Diabetes Sci. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1186\/s12911-021-01462-5","article-title":"Stacked lstm based deep recurrent neural network with kalman smoothing for blood glucose prediction","volume":"21","author":"Rabby","year":"2021","journal-title":"BMC Med. Inform. Decis. Mak."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11517-021-02437-4","article-title":"GLYFE: Review and benchmark of personalized glucose predictive models in type-1 diabetes","volume":"60","author":"Ammi","year":"2022","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wang, Y., and Wang, T. (2020). Application of improved lightgbm model in blood glucose prediction. Appl. Sci., 10.","DOI":"10.3390\/app10093227"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4206","DOI":"10.1038\/s41598-024-51438-4","article-title":"Pediatric diabetes prediction using deep learning","volume":"14","year":"2024","journal-title":"Sci. Rep."},{"key":"ref_18","first-page":"52","article-title":"An explainable hybrid deep learning model for prediabetes prediction in men aged 30 and above","volume":"20","author":"Nguyen","year":"2024","journal-title":"J. Men\u2019s Health"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1066744","DOI":"10.3389\/fcdhc.2022.1066744","article-title":"Hypoglycemia event prediction from cgm using ensemble learning","volume":"3","author":"Fleischer","year":"2022","journal-title":"Front. Clin. Diabetes Healthc."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"nwaf039","DOI":"10.1093\/nsr\/nwaf039","article-title":"Pretrained transformer model for decoding individual glucose dynamics from continuous glucose monitoring data","volume":"12","author":"Lu","year":"2025","journal-title":"Natl. Sci. Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"e26909","DOI":"10.2196\/26909","article-title":"Improved low-glucose predictive alerts based on sustained hypoglycemia: Model development and validation study","volume":"6","author":"Dave","year":"2021","journal-title":"JMIR Diabetes"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3101","DOI":"10.1109\/TBME.2020.2975959","article-title":"Benchmarking machine learning algorithms on blood glucose prediction for type i diabetes in comparison with classical time-series models","volume":"67","author":"Xie","year":"2020","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1213\/ANE.0000000000002864","article-title":"Correlation Coefficients: Appropriate Use and Interpretation","volume":"126","author":"Schober","year":"2018","journal-title":"Anesth. 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