Hybrid differential equations: Integrating mechanistic and data-driven techniques for modelling of water systems

Quaghebeur, Ward; Torfs, Elena; Baets, Bernard De

doi:10.1016/j.watres.2022.118166

Cited by 51 publications

(23 citation statements)

References 37 publications

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“…With Python being one of the most widely used programming languages (ranked #1 by IEEE Spectrum in 2021 (ref. 72)), QSDsan will benefit from the rapidly growing number of Python modules and libraries for future improvement (e.g., incorporation of machine learning in mechanistic modeling; 73 implementation of digital twin in water/wastewater utilities 74 ).…”

Section: Conclusion and Future Work Enabled By Qsdsanmentioning

confidence: 99%

QSDsan: an integrated platform for quantitative sustainable design of sanitation and resource recovery systems

Zhang

Morgan

et al. 2022

Environ. Sci.: Water Res. Technol.

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Section: Conclusion and Future Work Enabled By Qsdsanmentioning

confidence: 99%

QSDsan: an integrated platform for quantitative sustainable design of sanitation and resource recovery systems

Zhang

Morgan

et al. 2022

Environ. Sci.: Water Res. Technol.

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“…Two possible solutions exist to overcome the disadvantages of both mechanistic and data-driven models. A first very promising approach is the combination of both modelling paradigms into hybrid models (Lee et al 2005;Quaghebeur et al 2022). This creates a modelling paradigm that includes the best of both worlds: a mechanistic backbone incorporating relevant process knowledge and thus providing interpretability and extrapolation capabilities, as well as a data-driven part that augments the overall model's predictive power by including information on lesser-known subprocesses at reduced computational cost.…”

Section: Modelling Tools and Predictive Powermentioning

confidence: 99%

The transition of WRRF models to digital twin applications

Torfs

Nicolaï

Daneshgar

et al. 2022

Water Science and Technology

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Digital Twins (DTs) are on the rise as innovative, powerful technologies to harness the power of digitalisation in the WRRF sector. The lack of consensus and understanding when it comes to the definition, perceived benefits and technological needs of DTs is hampering their widespread development and application. Transitioning from traditional WRRF modelling practice into DT applications raises a number of important questions: When is a model's predictive power acceptable for a DT? Which modelling frameworks are most suited for DT applications? Which data structures are needed to efficiently feed data to a DT? How do we keep the DT up to date and relevant? Who will be the main users of DTs and how to get them involved? How do DTs push the water sector to evolve? This paper provides an overview of the state-of-the-art, challenges, good practices, development needs and transformative capacity of DTs for WRRF applications.

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“…The concept of neural differential equations [80,81], where the right-hand side of the differential equation, dx/dt = f (x; θ) is replaced by a neural network,…”

Section: Hybrid and Data Driven Modellingmentioning

confidence: 99%

Open Problems in Mathematical Biology

Vittadello¹,

Stumpf²

2022

Preprint

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Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life-and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.

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Hybrid differential equations: Integrating mechanistic and data-driven techniques for modelling of water systems

Cited by 51 publications

References 37 publications

QSDsan: an integrated platform for quantitative sustainable design of sanitation and resource recovery systems

QSDsan: an integrated platform for quantitative sustainable design of sanitation and resource recovery systems

The transition of WRRF models to digital twin applications

Open Problems in Mathematical Biology

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