{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T15:55:32Z","timestamp":1769010932240,"version":"3.49.0"},"reference-count":34,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,8]],"date-time":"2023-07-08T00:00:00Z","timestamp":1688774400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon 2020 research and innovation program","award":["870292"],"award-info":[{"award-number":["870292"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fermentation"],"abstract":"<jats:p>Hybrid modeling workflows combining machine learning with mechanistic process descriptions are becoming essential tools for bioprocess digitalization. In this study, a hybrid deep modeling method with state\u2013space reduction was developed and showcased with a P. pastoris GS115 Mut+ strain expressing a single-chain antibody fragment (scFv). Deep feedforward neural networks (FFNN) with varying depths were connected in series with bioreactor macroscopic material balance equations. The hybrid model structure was trained with a deep learning technique based on the adaptive moment estimation method (ADAM), semidirect sensitivity equations and stochastic regularization. A state\u2013space reduction method was investigated based on a principal component analysis (PCA) of the cumulative reacted amount. Data of nine fed-batch P. pastoris 50 L cultivations served to validate the method. Hybrid deep models were developed describing process dynamics as a function of critical process parameters (CPPs). The state\u2013space reduction method succeeded to decrease the hybrid model complexity by 60% and to improve the predictive power by 18.5% in relation to the nonreduced version. An exploratory design space analysis showed that the optimization of the feed of methanol and of inorganic elements has the potential to increase the scFv endpoint titer by 30% and 80%, respectively, in relation to the reference condition.<\/jats:p>","DOI":"10.3390\/fermentation9070643","type":"journal-article","created":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T01:02:50Z","timestamp":1688950970000},"page":"643","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Hybrid Deep Modeling of a GS115 (Mut+) Pichia pastoris Culture with State\u2013Space Reduction"],"prefix":"10.3390","volume":"9","author":[{"given":"Jos\u00e9","family":"Pinto","sequence":"first","affiliation":[{"name":"LAQV-REQUIMTE, Department of Chemistry, NOVA School of Science and Technology, NOVA University Lisbon, 2829-516 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6832-6774","authenticated-orcid":false,"given":"Jo\u00e3o R. C.","family":"Ramos","sequence":"additional","affiliation":[{"name":"LAQV-REQUIMTE, Department of Chemistry, NOVA School of Science and Technology, NOVA University Lisbon, 2829-516 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7539-488X","authenticated-orcid":false,"given":"Rafael S.","family":"Costa","sequence":"additional","affiliation":[{"name":"LAQV-REQUIMTE, Department of Chemistry, NOVA School of Science and Technology, NOVA University Lisbon, 2829-516 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8077-4177","authenticated-orcid":false,"given":"Rui","family":"Oliveira","sequence":"additional","affiliation":[{"name":"LAQV-REQUIMTE, Department of Chemistry, NOVA School of Science and Technology, NOVA University Lisbon, 2829-516 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,8]]},"reference":[{"key":"ref_1","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. 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