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The development of mechanistic models has been the traditional focus of BIOMATH. These models use first principles such as mass, energy, and momentum conservation to mathematically describe a process of interest. As such, the application can vary from fundamental research to full-scale plants, and everything in between.

Mechanistic models are attractive because they allow for the inference of causal relationships between process inputs and outputs. Additionally, they typically require a reduced amount of experimental data for calibration and validation purposes. However, a relatively high degree of specialised process knowledge is needed for the successful implementation of this approach.

BIOMATH has performed extensive research on, among others, computational fluid dynamics (CFD), population balance modelling (PBM), and bio-kinetics. CFD can be particularly valuable for the understanding of the intricate flow behaviours occurring in a wide variety of systems of industrial relevance (e.g., membrane bioreactors, activated sludge tanks, water distribution networks, etc.). In turn, PBM concerns itself with the prediction of the dynamic evolution of distributions (of flocs, granules, particles, bubbles, etc.), which makes it especially useful for the modelling of many processes such as granulation, coagulation-flocculation, and aeration. Finally, biokinetic models are used to describe the time-dependent evolution of biochemical species, which is fundamental for the understanding of yet another ample range of systems, such as anaerobic digestion, and (bio)pharmaceutical manufacturing.

Next to these (potentially coupled) methodologies, advanced model diagnostic tools such as global sensitivity and uncertainty analysis are extensively used by BIOMATH to construct robust models with high predictive power. Moreover, the knowledge collected by high-resolution (but computationally expensive) methods can be distilled and used to inform simpler and nimbler models and/or data-driven methodologies. The target application always determines the optimal approach.

Soft sensors play a key role in collecting qualitative and quantitative data for understanding technical and natural water systems. With soft sensors we mean physical sensors in combination with a model that usually estimates from a straightforward to measure variable another quantity of interest that is harder to measure. The obtained data can then be used for many interests within BIOMATH: To feed data hungry models such as data-driven and hybrid ones, inform digital twins in real time, for model predictive control or real time control, for calibration and validation of mechanistic models, and to gain insight into novel processes. Soft sensors can be deployed to create a dense network of measurements to also understand spatial distributions. Current research on this area includes the use of dynamical systems analysis for the development of robust soft sensors, and the estimation of inflow characteristics for the digital twin of the Tilburg wastewater treatment plant.

The water sector is transitioning towards a circular and digital future. To tackle the inherently multi-disciplinary and multi-objective challenges of future, we need a systemic approach for developing modelling and decision support tools that can provide us with a holistic and large-scale system optimisation. This means that such holistic digital twins for large-scale systems like cities and industrial areas need to overcome the interoperability challenge that comes when dealing with heterogeneous sources of data (e.g., water quality and quantity, energy, etc.) and coupling different models/sub-models of the system (e.g., for sewer networks, water/wastewater treatment, weather forecast, etc.). The concept of ontology and knowledge graph can help us to achieve this interoperability. An ontology is a conceptual model of the system that defines its concepts, objects and properties as well as the relationships between them. When data is mapped to the ontology, a knowledge graph is created that can be queried for information in a powerful and highly efficient way.

The use of ontology and knowledge graphs for developing holistic digital twins has never been properly explored in the water domain. Since 2023, and with the start of WaterFRAME FWO-SBO project, BIOMATH has been actively conducting state-of-the-art research on developing ontology-based digital twins for the water domain. The focus is on developing a dynamic knowledge graph of the physical system, with an over-arching layer of intelligent agents capable of running advanced and complex queries as well as large-scale simulations and optimisation. An example of a case study is the dynamic water reuse management and optimisation in an urban or industrial area where multiple sources of water can be allocated to different reuse purposes depending on their available quality/quantity and energetic, economic, and environmental aspects.