[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123341-en":3,"doc-seo-123341-105":30,"detail-sidebar-cat-0-en-105":95},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},123341,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Machine learning uncovers analytical kinetic models of bioprocesses - Abstract","Identifying suitable kinetic models for bioprocesses is difficult, especially when interpretable expressions are required. Conventional machine-learning methods often depend on assumed model structures and produce results that are hard to explain. This work uses symbolic regression to derive algebraic expressions for kinetic rates directly from concentration-profile data. Training follows a two-step procedure that avoids iterative differential-equation integration during parameter estimation. Numerical examples show performance slightly better than neural-network benchmarks, while the resulting rate equations support interpretation and enable direct optimization.","Chemical Engineering Science 300 (2024) 120606  \nContents lists available at ScienceDirect  \nChemical Engineering Science  \njournal [homepage: www.elsevier.com/locate/ces](homepage: www.elsevier.com/locate/ces)  \n| Machine learning uncovers analytical kinetic models of bioprocesses Tim Forster a, Daniel V´azquez b, Claudio Müllera, Gonzalo Guill´en-Gos´albez a,*\u003Cbr>a Department of Chemistry and Applied Biosciences, Institute for Chemical and Bioengineering, ETH Zurich, Vladimir-Prelog-Weg 1, 8093 Zurich, Switzerland b IQS School of Engineering, Universitat Ramon Llull, Via Augusta 390, 08017 Barcelona, Spain |  |  |  |\n| --- | --- | --- | --- |\n| A R T I C L E I N F O |  | A B S T R A C T |  |\n| Keywords: Bioprocess Symbolic regression Optimization |  | Identifying suitable kinetic models for bioprocesses is a complex task, particularly when interpretable models are sought. Classical machine learning algorithms are gaining wide interest to simulate complex bioprocesses that are hard to describe via first principles. However, they often rely on a priori assumptions of the model structure and lead to mathematical expressions that are hard to interpret. In this work, we apply an alternative approach based on symbolic regression to identify bioprocess models without assuming a pre-defined model structure. We obtain algebraic expressions for the kinetic rates from data consisting of concentration profiles. The model training was performed following a two-step approach that allows avoiding the iterative integration of differential equations for the parameter estimation step. The proposed procedure was found from numerical examples to slightly outperform neural network benchmarks. Moreover, the obtained algebraic expressions for the rate equations facilitate the model interpretation and enable the direct application of optimization algorithms. |  |\n\n1. Introduction  \nIn recent years, modelling has gained significant attention in the bioprocesses industry, spearheaded by the improvements in mathematical tools that can be used for analysis and optimization (Mowbray et al., 2023; Narayanan et al., 2021). Mathematical modelling can support scientists, engineers, or other subject matter experts in designing experiments (Sadino-Riquelme et al., 2020), predicting and monitoring processes (Del Rio-Chanona et al., 2019; Rivera et al., 2007), and reducing development and production costs (Narayanan et al., 2021, 2020). Modelling complex bioprocesses, however, is a challenging task, particularly when first principles formulations are sought (Mercier et al., 2014; Petsagkourakis et al., 2020; Zhang et al., 2020). These models are nevertheless being increasingly demanded by the market, in which the number of new products originating from bioprocesses is increasing very rapidly (Narayanan et al., 2023).  \nBioprocess modelling requires experimental measurements to calibrate an in-silico model by minimizing the mismatch between experimental observations and in-silico predictions. A common approach relies on well-established mathematical formalisms derived from first principles, such as mass or energy balances. Kroll et al. (2017) provide aworkflow for the generation of mechanistic process models, where the authors start from material balances for a certain target variable and expand the models in a mechanistic manner with new states and  \ninteractions. They used their method in a mammalian cell culture process to model the viable cell count. A more recent work by Sha et al.(2018) provides stoichiometric and kinetic models and some commonly used mathematical approaches to describe cell systems.  \nAn alternative to purely mechanistic modelling approaches are datadriven strategies. These methods enable model building without relying on expert knowledge (Kahrs and Marquardt, 2007; Taylor et al., 2021). Here, the structure of the model is given by the surrogate modelling approach of choice. For example in the area of process control, Willis et al. (1995)","cbCaib2qklHVH4cL","https://ap.wps.com/l/cbCaib2qklHVH4cL","pdf",2645391,1,13,"English","en",105,"# Introduction\n# Datadriven and hybrid modelling approaches\n# Symbolic regression methodology\n# Training procedure and parameter estimation\n# Numerical results and comparison","[{\"question\":\"Why is finding kinetic models for bioprocesses challenging when interpretability is needed?\",\"answer\":\"Kinetic model identification is complex because many classical approaches rely on predefined structures, which can yield expressions that are difficult to interpret.\"},{\"question\":\"How does symbolic regression help in this work?\",\"answer\":\"Symbolic regression identifies bioprocess models without assuming a pre-defined structure and produces algebraic expressions for kinetic rates from concentration-profile data.\"},{\"question\":\"What is the main advantage of the proposed training procedure?\",\"answer\":\"It uses a two-step approach that avoids iterative integration of differential equations during parameter estimation.\"},{\"question\":\"How do the derived rate equations support further use beyond interpretation?\",\"answer\":\"The algebraic rate expressions facilitate model interpretation and allow direct application of optimization algorithms.\"}]","Machine learning uncovers analytical kinetic models of bioprocesses - 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