{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T18:15:48Z","timestamp":1775758548109,"version":"3.50.1"},"reference-count":129,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T00:00:00Z","timestamp":1698019200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Associate Laboratory for Green Chemistry\u2014LAQV","award":["UIDB\/50006\/2020"],"award-info":[{"award-number":["UIDB\/50006\/2020"]}]},{"name":"Associate Laboratory for Green Chemistry\u2014LAQV","award":["UIDP\/50006\/2020"],"award-info":[{"award-number":["UIDP\/50006\/2020"]}]},{"name":"Associate Laboratory for Green Chemistry\u2014LAQV","award":["101099487- BioLaMer-HORIZON-EIC-2022-PATHFINDEROPEN-01"],"award-info":[{"award-number":["101099487- BioLaMer-HORIZON-EIC-2022-PATHFINDEROPEN-01"]}]},{"name":"the European Union\u2019s Horizon 2020","award":["UIDB\/50006\/2020"],"award-info":[{"award-number":["UIDB\/50006\/2020"]}]},{"name":"the European Union\u2019s Horizon 2020","award":["UIDP\/50006\/2020"],"award-info":[{"award-number":["UIDP\/50006\/2020"]}]},{"name":"the European Union\u2019s Horizon 2020","award":["101099487- BioLaMer-HORIZON-EIC-2022-PATHFINDEROPEN-01"],"award-info":[{"award-number":["101099487- BioLaMer-HORIZON-EIC-2022-PATHFINDEROPEN-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fermentation"],"abstract":"<jats:p>Deep learning is emerging in many industrial sectors in hand with big data analytics to streamline production. In the biomanufacturing sector, big data infrastructure is lagging compared to other industries. A promising approach is to combine deep neural networks (DNN) with prior knowledge in hybrid neural network (HNN) workflows that are less dependent on the quality and quantity of data. This paper reviews published articles over the past 30 years on the topic of HNN applications to bioprocesses. It reveals that HNNs have been applied to various bioprocesses, including microbial cultures, animal cells cultures, mixed microbial cultures, and enzyme biocatalysis. HNNs have been applied for process analysis, process monitoring, development of software sensors, open- and closed-loop control, batch-to-batch control, model predictive control, intensified design of experiments, quality-by-design, and recently for the development of digital twins. Most previous HNN studies have combined shallow feedforward neural networks (FFNNs) with physical laws, such as macroscopic material balance equations, following the semiparametric design principle. Only recently, deep HNNs based on deep FFNNs, convolution neural networks (CNN), long short-term memory (LSTM) networks and physics-informed neural networks (PINNs) have been reported. The biopharma sector is currently a major driver but applications to biologics quality attributes, new modalities, and downstream processing are significant research gaps.<\/jats:p>","DOI":"10.3390\/fermentation9100922","type":"journal-article","created":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T10:34:20Z","timestamp":1698057260000},"page":"922","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["From Shallow to Deep Bioprocess Hybrid Modeling: Advances and Future Perspectives"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8450-7954","authenticated-orcid":false,"given":"Roshanak","family":"Agharafeie","sequence":"first","affiliation":[{"name":"Nova Information Management School (NOVA IMS), NOVA University Lisbon, Campus de Campolide, 1070-312 Lisboa, Portugal"},{"name":"LAQV-REQUIMTE, Nova School of Science and Technology (NOVA-SST), NOVA University Lisbon, Campus da Caparica, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6832-6774","authenticated-orcid":false,"given":"Jo\u00e3o Rodrigues Correia","family":"Ramos","sequence":"additional","affiliation":[{"name":"LAQV-REQUIMTE, Nova School of Science and Technology (NOVA-SST), NOVA University Lisbon, Campus da Caparica, 2829-516 Caparica, Portugal"}]},{"given":"Jorge M.","family":"Mendes","sequence":"additional","affiliation":[{"name":"Nova Information Management School (NOVA IMS), NOVA University Lisbon, Campus de Campolide, 1070-312 Lisboa, Portugal"},{"name":"NOVA Cairo at The Knowledge Hub Universities, New Administrative Capital, Cairo 11835, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8077-4177","authenticated-orcid":false,"given":"Rui","family":"Oliveira","sequence":"additional","affiliation":[{"name":"LAQV-REQUIMTE, Nova School of Science and Technology (NOVA-SST), NOVA University Lisbon, Campus da Caparica, 2829-516 Caparica, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3309","DOI":"10.1016\/j.csbj.2020.10.018","article-title":"History and Evolution of Modeling in Biotechnology: Modeling & Simulation, Application and Hardware Performance","volume":"18","author":"Noll","year":"2020","journal-title":"Comput. Struct. Biotechnol. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1002\/bit.260190106","article-title":"Computer-aided Material Balancing for Prediction of Fermentation Parameters","volume":"19","author":"Cooney","year":"1977","journal-title":"Biotechnol. Bioeng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"727152","DOI":"10.3389\/fceng.2021.727152","article-title":"Towards Digitalization in Bio-Manufacturing Operations: A Survey on Application of Big Data and Digital Twin Concepts in Denmark","volume":"3","author":"Udugama","year":"2021","journal-title":"Front. Chem. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Yang, C.-T., Kristiani, E., Leong, Y.K., and Chang, J.-S. (2023). Big Data and Machine Learning Driven Bioprocessing\u2014Recent Trends and Critical Analysis. Bioresour. Technol., 372.","DOI":"10.1016\/j.biortech.2023.128625"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1016\/j.tibtech.2022.10.010","article-title":"Machine Learning in Bioprocess Development: From Promise to Practice","volume":"41","author":"Helleckes","year":"2023","journal-title":"Trends Biotechnol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1039\/D1RE00541C","article-title":"Industrial Data Science\u2014A Review of Machine Learning Applications for Chemical and Process Industries","volume":"7","author":"Mowbray","year":"2022","journal-title":"React. Chem. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Mowbray, M., Savage, T., Wu, C., Song, Z., Cho, B.A., Del Rio-Chanona, E.A., and Zhang, D. (2021). Machine Learning for Biochemical Engineering: A Review. Biochem. Eng. J., 172.","DOI":"10.1016\/j.bej.2021.108054"},{"key":"ref_8","unstructured":"Mitchell, T.M. (1997). Machine Learning, McGraw-Hill."},{"key":"ref_9","unstructured":"Kingma, D.P., and Ba, J.L. (2014). Adam: A Method for Stochastic Optimization. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1108\/SASBE-08-2021-0148","article-title":"An Investigation for Integration of Deep Learning and Digital Twins towards Construction 4.0","volume":"12","author":"Kor","year":"2023","journal-title":"Smart Sustain. Built Environ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6391","DOI":"10.1007\/s10462-021-09975-1","article-title":"A Systematic Review on Overfitting Control in Shallow and Deep Neural Networks","volume":"54","author":"Bejani","year":"2021","journal-title":"Artif. Intell. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1002\/aic.690381003","article-title":"A Hybrid Neural Network-first Principles Approach to Process Modeling","volume":"38","author":"Psichogios","year":"1992","journal-title":"AIChE J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1328","DOI":"10.1002\/aic.690400806","article-title":"Modeling Chemical Processes Using Prior Knowledge and Neural Networks","volume":"40","author":"Thompson","year":"1994","journal-title":"AIChE J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1002\/ceat.270170103","article-title":"Hybrid Modelling of Yeast Production Processes\u2014Combination of a Priori Knowledge on Different Levels of Sophistication","volume":"17","author":"Schubert","year":"1994","journal-title":"Chem. Eng. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0168-1656(94)90189-9","article-title":"Bioprocess Optimization and Control: Application of Hybrid Modelling","volume":"35","author":"Schubert","year":"1994","journal-title":"J. Biotechnol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/0098-1354(92)80053-C","article-title":"Hierarchical Neural Networks","volume":"16","author":"Mavrovouniotis","year":"1992","journal-title":"Comput. Chem. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"021705","DOI":"10.1115\/1.4042084","article-title":"Knowledge-Based Design of Artificial Neural Network Topology for Additive Manufacturing Process Modeling: A New Approach and Case Study for Fused Deposition Modeling","volume":"141","author":"Nagarajan","year":"2019","journal-title":"J. Mech. Des."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1016\/j.compchemeng.2004.02.014","article-title":"Combining First Principles Modelling and Artificial Neural Networks: A General Framework","volume":"28","author":"Oliveira","year":"2004","journal-title":"Comput. Chem. Eng."},{"key":"ref_19","unstructured":"Chen, R.T.Q., Rubanova, Y., Bettencourt, J., and Duvenaud, D. (2018). Neural Ordinary Differential Equations. arXiv."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Rackauckas, C., Ma, Y., Martensen, J., Warner, C., Zubov, K., Supekar, R., Skinner, D., Ramadhan, A., and Edelman, A. (2020). Universal Differential Equations for Scientific Machine Learning. arXiv.","DOI":"10.21203\/rs.3.rs-55125\/v1"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1016\/0043-1354(95)93250-W","article-title":"Dynamic Modelling of the Activated Sludge Process: Improving Prediction Using Neural Networks","volume":"29","author":"Grandjean","year":"1995","journal-title":"Water Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1016\/S0098-1354(96)00332-8","article-title":"Application of Artificial Neural Networks for Crossflow Microfiltration Modelling: \u201cBlack-Box\u201d and Semi-Physical Approaches","volume":"21","author":"Piron","year":"1997","journal-title":"Comput. Chem. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1016\/S0098-1354(01)00665-2","article-title":"Knowledge Based Modular Networks for Process Modelling and Control","volume":"25","author":"Peres","year":"2001","journal-title":"Comput. Chem. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Richman, R., and Wuthrich, M.V. (2023). Smoothness and Monotonicity Constraints for Neural Networks Using ICEnet. SSRN Electron. J.","DOI":"10.2139\/ssrn.4449030"},{"key":"ref_25","first-page":"21","article-title":"A Case for New Neural Network Smoothness Constraints","volume":"137","author":"Rosca","year":"2020","journal-title":"Proc. Mach. Learn. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations","volume":"378","author":"Raissi","year":"2019","journal-title":"J. Comput. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"109951","DOI":"10.1016\/j.jcp.2020.109951","article-title":"NSFnets (Navier-Stokes Flow Nets): Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equations","volume":"426","author":"Jin","year":"2021","journal-title":"J. Comput. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"10862","DOI":"10.1016\/j.eswa.2011.02.117","article-title":"A Novel Identification Method for Hybrid (N)PLS Dynamical Systems with Application to Bioprocesses","volume":"38","author":"Oliveira","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1007\/s00449-019-02181-y","article-title":"A Bootstrap-Aggregated Hybrid Semi-Parametric Modeling Framework for Bioprocess Development","volume":"42","author":"Pinto","year":"2019","journal-title":"Bioprocess Biosyst. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"107952","DOI":"10.1016\/j.compchemeng.2022.107952","article-title":"A General Deep Hybrid Model for Bioreactor Systems: Combining First Principles with Deep Neural Networks","volume":"165","author":"Pinto","year":"2022","journal-title":"Comput. Chem. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/j.jbiotec.2007.08.020","article-title":"Hybrid Semi-Parametric Mathematical Systems: Bridging the Gap between Systems Biology and Process Engineering","volume":"132","author":"Teixeira","year":"2007","journal-title":"J. Biotechnol."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Pinto, J., Costa, R.S., Alexandre, L., Ramos, J., and Oliveira, R. (2023). SBML2HYB: A Python Interface for SBML Compatible Hybrid Modeling. Bioinformatics, 39.","DOI":"10.1093\/bioinformatics\/btad044"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"303","DOI":"10.3390\/ai4010014","article-title":"A General Hybrid Modeling Framework for Systems Biology Applications: Combining Mechanistic Knowledge with Deep Neural Networks under the SBML Standard","volume":"4","author":"Pinto","year":"2023","journal-title":"AI"},{"key":"ref_34","first-page":"105906","article-title":"The PRISMA 2020 Statement: An Updated Guideline for Reporting Systematic Reviews","volume":"372","author":"Page","year":"2021","journal-title":"BMJ"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"264","DOI":"10.7326\/0003-4819-151-4-200908180-00135","article-title":"Guidelines and Guidance Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA Statement","volume":"151","author":"Moher","year":"2009","journal-title":"Ann. Intern. Med."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/j.cherd.2022.01.041","article-title":"Il Physics-Informed Neural Networks for Hybrid Modeling of Lab-Scale Batch Fermentation for \u03b2-Carotene Production Using Saccharomyces Cerevisiae","volume":"179","author":"Bangi","year":"2022","journal-title":"Chem. Eng. Res. Des."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"107736","DOI":"10.1016\/j.compchemeng.2022.107736","article-title":"HybridML: Open Source Platform for Hybrid Modeling","volume":"160","author":"Merkelbach","year":"2022","journal-title":"Comput. Chem. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"135643","DOI":"10.1016\/j.cej.2022.135643","article-title":"Deep Neural Network-Based Hybrid Modeling and Experimental Validation for an Industry-Scale Fermentation Process: Identification of Time-Varying Dependencies among Parameters","volume":"441","author":"Shah","year":"2022","journal-title":"Chem. Eng. J."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"7185","DOI":"10.1007\/s00521-021-06499-1","article-title":"Knowledge and Data-Driven Hybrid System for Modeling Fuzzy Wastewater Treatment Process","volume":"35","author":"Cheng","year":"2023","journal-title":"Neural Comput. Appl."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.compchemeng.2013.08.008","article-title":"Hybrid Semi-Parametric Modeling in Process Systems Engineering: Past, Present and Future","volume":"60","author":"Oliveira","year":"2014","journal-title":"Comput. Chem. Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1002\/bit.10247","article-title":"Hybrid Neural Network Modeling of a Full-Scale Industrial Wastewater Treatment Process","volume":"78","author":"Lee","year":"2002","journal-title":"Biotechnol. Bioeng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/S0960-8524(00)00106-1","article-title":"Simulation of Biomass Gasification with a Hybrid Neural Network Model","volume":"76","author":"Guo","year":"2001","journal-title":"Bioresour. Technol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1111\/j.1472-765X.2006.02038.x","article-title":"Optimization for High-Density Cultivation of Heterotrophic Chlorella Based on a Hybrid Neural Network Model","volume":"44","author":"Wu","year":"2007","journal-title":"Lett. Appl. Microbiol."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Teixeira, A.P., Alves, C., Alves, P.M., Carrondo, M.J.T., and Oliveira, R. (2007). Hybrid Elementary Flux Analysis\/Nonparametric Modeling: Application for Bioprocess Control. BMC Bioinform., 8.","DOI":"10.1186\/1471-2105-8-30"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"416","DOI":"10.2533\/chimia.1996.416","article-title":"The Use of Hybrid Modelling for the Optimization of the Penicillin Fermentation Process","volume":"50","author":"Preusting","year":"1996","journal-title":"Chimia"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"S859","DOI":"10.1016\/S0098-1354(98)00166-5","article-title":"An Adaptive Optimal Control Scheme Based on Hybrid Neural Modelling","volume":"22","author":"Costa","year":"1998","journal-title":"Comput. Chem. Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1590\/S0104-66321999000100006","article-title":"Hybrid Neural Model for the Optimization of Fed-Batch Fermentations","volume":"16","author":"Costa","year":"1999","journal-title":"Braz. J. Chem. Eng."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1385\/ABAB:98-100:1-9:1009","article-title":"Hybrid Neural Modeling of Bioprocesses Using Functional Link Networks","volume":"98\u2013100","author":"Harada","year":"2002","journal-title":"Appl. Biochem. Biotechnol. Part A Enzym. Eng. Biotechnol."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1590\/S0104-66322000000400063","article-title":"State and Parameter Estimation Based on a Nonlinear Filter Applied to an Industrial Process Control of Ethanol Production","volume":"17","author":"Meleiro","year":"2000","journal-title":"Braz. J. Chem. Eng."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1385\/ABAB:77:1-3:277","article-title":"A Hybrid Neural Model of Ethanol Production by Zymomonas Mobilis","volume":"77\u201379","author":"Henriques","year":"1999","journal-title":"Appl. Biochem. Biotechnol."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/S1474-6670(17)40200-X","article-title":"Hybnet, an Advanced Tool for Process Optimization and Control","volume":"331","author":"Oliveira","year":"1998","journal-title":"IFAC Proc."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/S0168-1656(97)00166-1","article-title":"How to Increase the Performance of Models for Process Optimization and Control","volume":"59","author":"Simutis","year":"1997","journal-title":"J. Biotechnol."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s00449-020-02445-y","article-title":"Hybrid Neural Network Modeling and Particle Swarm Optimization for Improved Ethanol Production from Cashew Apple Juice","volume":"44","author":"Pinheiro","year":"2021","journal-title":"Bioprocess Biosyst. Eng."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1007\/s00449-013-1029-9","article-title":"Fast Development of Pichia Pastoris GS115 Mut+ Cultures Employing Batch-to-Batch Control and Hybrid Semi-Parametric Modeling","volume":"37","author":"Ferreira","year":"2014","journal-title":"Bioprocess Biosyst. Eng."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1021\/bp0502328","article-title":"Bioprocess Iterative Batch-to-Batch Optimization Based on Hybrid Parametric\/Nonparametric Models","volume":"22","author":"Teixeira","year":"2006","journal-title":"Biotechnol. Prog."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1002\/elsc.201600037","article-title":"Intensified Design of Experiments for Upstream Bioreactors","volume":"17","author":"Willis","year":"2017","journal-title":"Eng. Life Sci."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1002\/btpr.2295","article-title":"Toward Intensifying Design of Experiments in Upstream Bioprocess Development: An Industrial Escherichia Coli Feasibility Study","volume":"32","author":"Hamelink","year":"2016","journal-title":"Biotechnol. Prog."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Bayer, B., von Stosch, M., Striedner, G., and Duerkop, M. (2020). Comparison of Modeling Methods for DoE-Based Holistic Upstream Process Characterization. Biotechnol. J., 15.","DOI":"10.1002\/biot.201900551"},{"key":"ref_59","first-page":"321","article-title":"Towards Risk-Aware Machine Learning Supported Model Predictive Control and Open-Loop Optimization for Repetitive Processes","volume":"54","author":"Morabito","year":"2021","journal-title":"IFAC Pap."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"183","DOI":"10.15255\/CABEQ.2014.2101","article-title":"Mathematical Modelling as a Tool for Optimized PHA Production","volume":"29","author":"Novak","year":"2015","journal-title":"Chem. Biochem. Eng. Q."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/s11947-008-0086-6","article-title":"Design Considerations in Hybrid Neural Optimization of Fed-Batch Fermentation for PHB Production by Ralstonia Eutropha","volume":"3","author":"Patnaik","year":"2010","journal-title":"Food Bioprocess Technol."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1016\/S1570-7946(04)80188-3","article-title":"Hybrid Modelling of a PHA Production Process Using Modular Neural Networks","volume":"18","author":"Peres","year":"2004","journal-title":"Comput. Aided Chem. Eng."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/j.bej.2007.09.003","article-title":"Bioprocess Hybrid Parametric\/Nonparametric Modelling Based on the Concept of Mixture of Experts","volume":"39","author":"Peres","year":"2008","journal-title":"Biochem. Eng. J."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1080\/10889860802261687","article-title":"Neural and Hybrid Optimizations of the Fed-Batch Synthesis of Poly-\u03b2-Hydroxybutyrate by Ralstonia Eutropha in a Nonideal Bioreactor","volume":"12","author":"Patnaik","year":"2008","journal-title":"Bioremediat. J."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Luna, M.F., Ochsner, A.M., Amstutz, V., von Blarer, D., Sokolov, M., Arosio, P., and Zinn, M. (2021). Modeling of Continuous PHA Production by a Hybrid Approach Based on First Principles and Machine Learning. Processes, 9.","DOI":"10.3390\/pr9091560"},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Bayer, B., Striedner, G., and Duerkop, M. (2020). Hybrid Modeling and Intensified DoE: An Approach to Accelerate Upstream Process Characterization. Biotechnol. J., 15.","DOI":"10.1002\/biot.202000121"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"117064","DOI":"10.1016\/j.seppur.2020.117064","article-title":"Hybrid Modeling of Cross-Flow Filtration: Predicting the Flux Evolution and Duration of Ultrafiltration Processes","volume":"248","author":"Krippl","year":"2020","journal-title":"Sep. Purif. Technol."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"2703","DOI":"10.1002\/bit.27437","article-title":"Hybrid-EKF: Hybrid Model Coupled with Extended Kalman Filter for Real-Time Monitoring and Control of Mammalian Cell Culture","volume":"117","author":"Narayanan","year":"2020","journal-title":"Biotechnol. Bioeng."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"696","DOI":"10.1002\/btpr.2435","article-title":"Optimization of Biopharmaceutical Downstream Processes Supported by Mechanistic Models and Artificial Neural Networks","volume":"33","author":"Pirrung","year":"2017","journal-title":"Biotechnol. Prog."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1002\/biot.201300385","article-title":"Hybrid Modeling for Quality by Design and PAT-Benefits and Challenges of Applications in Biopharmaceutical Industry","volume":"9","author":"Davy","year":"2014","journal-title":"Biotechnol. J."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1007\/s00449-016-1557-1","article-title":"Hybrid Modeling as a QbD\/PAT Tool in Process Development: An Industrial E. coli Case Study","volume":"39","author":"Hamelink","year":"2016","journal-title":"Bioprocess Biosyst. Eng."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/S1474-6670(17)45604-7","article-title":"Advanced Supervision of Mammalian Cell Cultures Using Hybrid Process Models","volume":"28","author":"Dors","year":"1995","journal-title":"IFAC Proc. Vol."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1016\/0098-1354(95)00190-5","article-title":"A Hybrid Neural Network\u2014First Principles Approach for Modelling of Cell Metabolism","volume":"20","author":"Fu","year":"1996","journal-title":"Comput. Chem. Eng."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.jbiotec.2005.04.024","article-title":"Modelling and Optimization of a Recombinant BHK-21 Cultivation Process Using Hybrid Grey-Box Systems","volume":"118","author":"Teixeira","year":"2005","journal-title":"J. Biotechnol."},{"key":"ref_75","doi-asserted-by":"crossref","unstructured":"Maton, M., Bogaerts, P., and Vande Wouwer, A. (2022). Hybrid Dynamic Models of Bioprocesses Based on Elementary Flux Modes and Multilayer Perceptrons. Processes, 10.","DOI":"10.3390\/pr10102084"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/s10616-010-9291-z","article-title":"Comparison of Viable Cell Concentration Estimation Methods for a Mammalian Cell Cultivation Process","volume":"62","author":"Aehle","year":"2010","journal-title":"Cytotechnology"},{"key":"ref_77","doi-asserted-by":"crossref","unstructured":"Narayanan, H., Luna, M.F., von Stosch, M., Cruz Bournazou, M.N., Polotti, G., Morbidelli, M., Butt\u00e9, A., and Sokolov, M. (2020). Bioprocessing in the Digital Age: The Role of Process Models. Biotechnol. J., 15.","DOI":"10.1002\/biot.201900172"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"e00131","DOI":"10.1016\/j.mec.2020.e00131","article-title":"Harnessing the Potential of Artificial Neural Networks for Predicting Protein Glycosylation","volume":"10","author":"Kotidis","year":"2020","journal-title":"Metab. Eng. Commun."},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Bayer, B., Duerkop, M., Striedner, G., and Sissolak, B. (2021). Model Transferability and Reduced Experimental Burden in Cell Culture Process Development Facilitated by Hybrid Modeling and Intensified Design of Experiments. Front. Bioeng. Biotechnol., 9.","DOI":"10.3389\/fbioe.2021.740215"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1061\/(ASCE)0733-9372(1997)123:4(311)","article-title":"Modeling Nutrient Dynamics in Sequencing Batch Reactor","volume":"123","author":"Zhao","year":"1997","journal-title":"J. Environ. Eng."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"1694","DOI":"10.1021\/ie990557r","article-title":"Use of Hybrid Models in Wastewater Systems","volume":"39","author":"Anderson","year":"2000","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_82","first-page":"6","article-title":"Prediction Method for Wastewater COD Based on Hybrid Neural Network Model","volume":"19","author":"Fang","year":"2003","journal-title":"Zhongguo Jishui Paishui\/China Water Wastewater"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s00449-005-0031-2","article-title":"The Study of Neural Network-Based Controller for Controlling Dissolved Oxygen Concentration in a Sequencing Batch Reactor","volume":"28","author":"Azwar","year":"2006","journal-title":"Bioprocess Biosyst. Eng."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"1717","DOI":"10.1016\/S1570-7946(06)80295-6","article-title":"Hybrid Modular Mechanistic\/ANN Modelling of a Wastewater Phosphorus Removal Process","volume":"21","author":"Peres","year":"2006","journal-title":"Comput. Aided Chem. Eng."},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Xiao, J., Liu, C., Ju, B., Xu, H., Sun, D., and Dang, Y. (2021). Estimation of In-Situ Biogas Upgrading in Microbial Electrolysis Cells via Direct Electron Transfer: Two-Stage Machine Learning Modeling Based on a NARX-BP Hybrid Neural Network. Bioresour. Technol., 330.","DOI":"10.1016\/j.biortech.2021.124965"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1002\/(SICI)1097-0290(19990320)62:6<666::AID-BIT6>3.0.CO;2-S","article-title":"An Efficient Model Development Strategy for Bioprocesses Based on Neural Networks in Macroscopic Balances: Part II","volume":"62","author":"Bijman","year":"1999","journal-title":"Biotechnol. Bioeng."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1002\/aic.690440507","article-title":"Understanding and Applying the Extrapolation Properties of Serial Gray-Box Models","volume":"44","author":"Dubbclman","year":"1998","journal-title":"AIChE J."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"1761","DOI":"10.1007\/s11274-008-9670-1","article-title":"Use of Neural Networks in the Mathematical Modelling of the Enzymic Synthesis of Amoxicillin Catalysed by Penicillin G Acylase Immobilized in Chitosan","volume":"24","author":"Silva","year":"2008","journal-title":"World J. Microbiol. Biotechnol."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.memsci.2007.05.024","article-title":"Analysis of Solvent Flux through Nanofiltration Membranes by Mechanistic, Chemometric and Hybrid Modelling","volume":"300","author":"Santos","year":"2007","journal-title":"J. Memb. Sci."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"7155","DOI":"10.1021\/ef301452s","article-title":"Biomass Leachate Treatment and Nutrient Recovery Using Reverse Osmosis: Experimental Study and Hybrid Artificial Neural Network Modeling","volume":"26","author":"Rajabzadeh","year":"2012","journal-title":"Energy Fuels"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1021\/bp034026g","article-title":"A Hybrid Model Framework for the Optimization of Preparative Chromatographic Processes","volume":"20","author":"Nagrath","year":"2004","journal-title":"Biotechnol. Prog."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.chroma.2017.07.089","article-title":"Root Cause Investigation of Deviations in Protein Chromatography Based on Mechanistic Models and Artificial Neural Networks","volume":"1515","author":"Wang","year":"2017","journal-title":"J. Chromatogr. A"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"462248","DOI":"10.1016\/j.chroma.2021.462248","article-title":"Hybrid Models for the Simulation and Prediction of Chromatographic Processes for Protein Capture","volume":"1650","author":"Narayanan","year":"2021","journal-title":"J. Chromatogr. A"},{"key":"ref_94","doi-asserted-by":"crossref","unstructured":"Pinto, J., Ramos, J.R.C., Costa, R.S., Rossell, S., Dumas, P., and Oliveira, R. (2023). Hybrid Deep Modeling of a CHO-K1 Fed-Batch Process: Combining First-Principles with Deep Neural Networks. Front. Bioeng. Biotechnol., 11.","DOI":"10.3389\/fbioe.2023.1237963"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"e16980","DOI":"10.1002\/aic.16980","article-title":"Operable Adaptive Sparse Identification of Systems: Application to Chemical Processes","volume":"66","author":"Bhadriraju","year":"2020","journal-title":"AIChE J."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"e18012","DOI":"10.1002\/aic.18012","article-title":"Deep Hybrid Model-Based Predictive Control with Guarantees on Domain of Applicability","volume":"69","author":"Bangi","year":"2023","journal-title":"AIChE J."},{"key":"ref_97","doi-asserted-by":"crossref","unstructured":"Shah, P., Choi, H.-K., and Kwon, J.S.-I. (2023). Achieving Optimal Paper Properties: A Layered Multiscale KMC and LSTM-ANN-Based Control Approach for Kraft Pulping. Processes, 11.","DOI":"10.3390\/pr11030809"},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"e17946","DOI":"10.1002\/aic.17946","article-title":"Multi-Rate Observer Design and Optimal Control to Maximize Productivity of an Industry-Scale Fermentation Process","volume":"69","author":"Shah","year":"2023","journal-title":"AIChE J."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"1662","DOI":"10.1126\/science.1069492","article-title":"Systems Biology: A Brief Overview","volume":"295","author":"Kitano","year":"2002","journal-title":"Science"},{"key":"ref_100","doi-asserted-by":"crossref","unstructured":"Zampieri, G., Vijayakumar, S., Yaneske, E., and Angione, C. (2019). Machine and Deep Learning Meet Genome-Scale Metabolic Modeling. PLoS Comput. Biol., 15.","DOI":"10.1371\/journal.pcbi.1007084"},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.copbio.2019.11.007","article-title":"Recent Advances on Constraint-Based Models by Integrating Machine Learning","volume":"64","author":"Rana","year":"2020","journal-title":"Curr. Opin. Biotechnol."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s43393-022-00115-6","article-title":"Advances and Applications of Machine Learning and Intelligent Optimization Algorithms in Genome-Scale Metabolic Network Models","volume":"3","author":"Bai","year":"2023","journal-title":"Syst. Microbiol. Biomanufacturing"},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"1889","DOI":"10.1007\/s00449-022-02795-9","article-title":"Genome-Scale Modeling of Chinese Hamster Ovary Cells by Hybrid Semi-Parametric Flux Balance Analysis","volume":"45","author":"Ramos","year":"2022","journal-title":"Bioprocess Biosyst. Eng."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"4669","DOI":"10.1038\/s41467-023-40380-0","article-title":"A Neural-Mechanistic Hybrid Approach Improving the Predictive Power of Genome-Scale Metabolic Models","volume":"14","author":"Faure","year":"2023","journal-title":"Nat. Commun."},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"e16925","DOI":"10.1002\/aic.16925","article-title":"Identification of Cell-to-Cell Heterogeneity through Systems Engineering Approaches","volume":"66","author":"Lee","year":"2020","journal-title":"AIChE J."},{"key":"ref_106","doi-asserted-by":"crossref","unstructured":"Lee, D., Jayaraman, A., and Kwon, J.S. (2020). Development of a Hybrid Model for a Partially Known Intracellular Signaling Pathway through Correction Term Estimation and Neural Network Modeling. PLoS Comput. Biol., 16.","DOI":"10.1371\/journal.pcbi.1008472"},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"112789","DOI":"10.1016\/j.cma.2019.112789","article-title":"Physics-Informed Neural Networks for High-Speed Flows","volume":"360","author":"Mao","year":"2020","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1038\/s42254-021-00314-5","article-title":"Physics-Informed Machine Learning","volume":"3","author":"Karniadakis","year":"2021","journal-title":"Nat. Rev. Phys."},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"2072","DOI":"10.1002\/bit.28503","article-title":"Hybrid Modeling in Bioprocess Dynamics: Structural Variabilities, Implementation Strategies, and Practical Challenges","volume":"120","author":"Mahanty","year":"2023","journal-title":"Biotechnol. Bioeng."},{"key":"ref_110","unstructured":"Hao, Z., Liu, S., Zhang, Y., Ying, C., Feng, Y., Su, H., and Zhu, J. (2022). Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications. arXiv."},{"key":"ref_111","unstructured":"Cui, T., Bertalan, T.S., Ndahiro, N., Khare, P., Betenbaugh, M., Maranas, C., and Kevrekidis, I.G. (2023). Data-Driven and Physics Informed Modelling of Chinese Hamster Ovary Cell Bioreactors. arXiv."},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/B978-0-443-15274-0.50014-7","article-title":"Investigating Physics-Informed Neural Networks for Bioprocess Hybrid Model Construction","volume":"52","author":"Rogers","year":"2023","journal-title":"Comput. Aided Chem. Eng."},{"key":"ref_113","doi-asserted-by":"crossref","unstructured":"Lagergren, J.H., Nardini, J.T., Baker, R.E., Simpson, M.J., and Flores, K.B. (2020). Biologically-Informed Neural Networks Guide Mechanistic Modeling from Sparse Experimental Data. PLoS Comput. Biol., 16.","DOI":"10.1371\/journal.pcbi.1008462"},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1002\/jctb.4477","article-title":"Mini-Review: Soft Sensors as Means for PAT in the Manufacture of Bio-Therapeutics","volume":"90","author":"Mandenius","year":"2015","journal-title":"J. Chem. Technol. Biotechnol."},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1016\/j.biotechadv.2009.05.003","article-title":"Advances in On-Line Monitoring and Control of Mammalian Cell Cultures: Supporting the PAT Initiative","volume":"27","author":"Teixeira","year":"2009","journal-title":"Biotechnol. Adv."},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1002\/btpr.706","article-title":"Hybrid Modeling Framework for Process Analytical Technology: Application to Bordetella Pertussis Cultures","volume":"28","author":"Oliveria","year":"2012","journal-title":"Biotechnol. Prog."},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1007\/s10295-020-02308-1","article-title":"Towards Smart Biomanufacturing: A Perspective on Recent Developments in Industrial Measurement and Monitoring Technologies for Bio-Based Production Processes","volume":"47","author":"Gargalo","year":"2020","journal-title":"J. Ind. Microbiol. Biotechnol."},{"key":"ref_118","doi-asserted-by":"crossref","unstructured":"Von Stosch, M., Schenkendorf, R., Geldhof, G., Varsakelis, C., Mariti, M., Dessoy, S., Vandercammen, A., Pysik, A., and Sanders, M. (2020). Working within the Design Space: Do Our Static Process Characterization Methods Suffice?. Pharmaceutics, 12.","DOI":"10.3390\/pharmaceutics12060562"},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"107365","DOI":"10.1016\/j.compchemeng.2021.107365","article-title":"Recent Trends on Hybrid Modeling for Industry 4.0","volume":"151","author":"Sansana","year":"2021","journal-title":"Comput. Chem. Eng."},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"147138","DOI":"10.1016\/j.scitotenv.2021.147138","article-title":"A Machine Learning Framework to Improve Effluent Quality Control in Wastewater Treatment Plants","volume":"784","author":"Wang","year":"2021","journal-title":"Sci. Total Environ."},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"3356","DOI":"10.1002\/bit.27512","article-title":"Combining Model Structure Identification and Hybrid Modelling for Photo-Production Process Predictive Simulation and Optimisation","volume":"117","author":"Zhang","year":"2020","journal-title":"Biotechnol. Bioeng."},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"11709","DOI":"10.1038\/s41598-022-15416-y","article-title":"Learning Transport Processes with Machine Intelligence","volume":"12","author":"Miniati","year":"2022","journal-title":"Sci. Rep."},{"key":"ref_123","doi-asserted-by":"crossref","unstructured":"Sitapure, N., and Kwon, J.S. (2023). Introducing Hybrid Modeling with Time-Series-Transformers: A Comparative Study of Series and Parallel Approach in Batch Crystallization. arXiv.","DOI":"10.1021\/acs.iecr.3c02624"},{"key":"ref_124","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/j.cherd.2023.04.028","article-title":"Exploring the Potential of Time-Series Transformers for Process Modeling and Control in Chemical Systems: An Inevitable Paradigm Shift?","volume":"194","author":"Sitapure","year":"2023","journal-title":"Chem. Eng. Res. Des."},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"108339","DOI":"10.1016\/j.compchemeng.2023.108339","article-title":"CrystalGPT: Enhancing System-to-System Transferability in Crystallization Prediction and Control Using Time-Series-Transformers","volume":"177","author":"Sitapure","year":"2023","journal-title":"Comput. Chem. Eng."},{"key":"ref_126","doi-asserted-by":"crossref","first-page":"10466","DOI":"10.1021\/acs.iecr.1c01317","article-title":"Hybrid Models Based on Machine Learning and an Increasing Degree of Process Knowledge: Application to Capture Chromatographic Step","volume":"60","author":"Narayanan","year":"2021","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_127","doi-asserted-by":"crossref","first-page":"5929","DOI":"10.1021\/acs.iecr.2c04355","article-title":"Can a Computer \u201cLearn\u201d Nonlinear Chromatography?: Experimental Validation of Physics-Based Deep Neural Networks for the Simulation of Chromatographic Processes","volume":"62","author":"Subraveti","year":"2023","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_128","doi-asserted-by":"crossref","unstructured":"Bourl\u00e8s, E., de Lannoy, G., Scutell\u00e0, B., Fonseca, F., Trelea, I.C., and Passot, S. (2019). Scale-up of Freeze-Drying Cycles, the Use of Process Analytical Technology (PAT), and Statistical Analysis, Humana Press.","DOI":"10.1007\/978-1-4939-8928-7_10"},{"key":"ref_129","unstructured":"Smyth, P., de Lannoy, G., Von Stosch, M., Pysik, A., and Khan, A. (2019, January 24\u201326). Machine Learning in Research and Development of New Vaccines Products: Opportunities and Challenges. Proceedings of the ESANN 2019\u2014Proceedings, 27th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, Bruges, Belgium."}],"container-title":["Fermentation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2311-5637\/9\/10\/922\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:10:29Z","timestamp":1760130629000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2311-5637\/9\/10\/922"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,23]]},"references-count":129,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["fermentation9100922"],"URL":"https:\/\/doi.org\/10.3390\/fermentation9100922","relation":{},"ISSN":["2311-5637"],"issn-type":[{"value":"2311-5637","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,23]]}}}