
Such approaches can improve reliability or resilience for future changes. Conservative design and operation, employing high safety margins, typically lead to oversized plants and energy-intensive processes, resulting in increased costs and resource consumption. This goal can be reached by operating within defined safety margins or through adequate monitoring, control, and interventions, or a combination of the two. Urban water management has a critical function for maintaining human and environmental health by ensuring potable water quality and treated wastewater. HM is a paradigm for WRRF modelling to transition towards a more resource-efficient, resilient, and sustainable future.
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We also highlight challenges and research needs for HM design and architecture, good modelling practice, data assurance, and software compatibility. This article presents an overview of HM methodologies applied to WRRFs and aims to stimulate the wider adoption and development of HM.
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Despite the potential of HM in a sector that is undergoing a significant digital and cultural transformation, the application of hybrid models remains vague. Hybrid modelling (HM) combines these two modelling paradigms and aims to leverage both the rapidly increasing volumes of data collected, as well as the continued pursuit of greater process understanding.

Recent advances in data-driven methods have provided options for harnessing the power of Industry 4.0, but they are often limited by the lack of interpretability and extrapolation capabilities. Despite the successful application of mechanistic models in the water sector, they show some important limitations and do not fully profit from the increasing digitalisation of systems and processes.

Mathematical modelling is an indispensable tool to support water resource recovery facility (WRRF) operators and engineers with the ambition of creating a truly circular economy and assuring a sustainable future.
