Mathematical modelling of bioprocesses has a long and notable history, with eminent contributions from fields including microbiology, ecology, biophysics, chemistry, statistics, control theory and mathematical theory. This richness of ideas and breadth of concepts provide great motivation for inquisitive engineers and intrepid scientists to try their hand at modelling, and this collaboration of disciplines has also delivered significant milestones in the quality and application of models for both theoretical and practical interrogation of engineered biological systems. The focus of this review is the anaerobic digestion process, which, as a technology that has come in and out of fashion, remains a fundamental process for addressing the global climate emergency. Whether with conventional anaerobic digestion systems, biorefineries, or other anaerobic technologies, mathematical models are important tools that are used to design, monitor, control and optimise the process. Both highly structured, mechanistic models and data-driven approaches have been used extensively over half a decade, but recent advances in computational capacity, scientific understanding and diversity and quality of process data, presents an opportunity for the development of new modelling paradigms, augmentation of existing methods, or even incorporation of tools from other disciplines, to ensure that anaerobic digestion research can remain resilient and relevant in the face of emerging and future challenges.
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