Workshop on Mathematical Challenges in Industry

Urban wastewater treatment plants are major energy consumers, with pumping systems accounting for a significant share of total electricity use. While these systems are essential to ensure stable and reliable operation, they are often managed using simple control strategies that do not take energy efficiency into account.

The challenge focuses on the intelligent operation of a pumping station equipped with multiple pumps. The objective is to develop a mathematical and computational approach that minimises energy consumption while ensuring stable flow conditions and respecting operational constraints. The solution should account for varying inflows, different pump characteristics, and decisions over a future time horizon, combining pump activation and operating frequencies in an optimal way.

This challenge invites participants to formulate the problem, define appropriate constraints and objectives, and propose an optimisation strategy capable of supporting more energy-efficient and proactive operation of wastewater pumping systems.

Wastewater treatment plants are essential for environmental protection and public health, yet their operation is governed by complex, nonlinear biological dynamics and stringent regulatory constraints. While detailed mechanistic models are available, their complexity often hinders the direct application of advanced control techniques.

This challenge focuses on the identification of reduced-order, data-driven dynamical models—such as linear state-space representations—derived from input–output data of a wastewater treatment process. These models are intended to approximate the system dynamics around a given operating point and to serve as the basis for control design.

Participants are invited to use the identified models within a model predictive control (MPC) framework to regulate key effluent quality indicators while minimising operational costs, in particular energy consumption. The challenge highlights the interplay between system identification, model reduction, optimisation, and predictive control, illustrating how mathematical methods can support efficient and reliable operation of wastewater treatment systems.

Detailed mechanistic models are widely used to represent the biological processes involved in urban wastewater treatment. While these models provide high-fidelity descriptions of plant dynamics, their complexity often limits their direct use in optimisation and control tasks.

This challenge focuses on the mathematical modelling problem itself, rather than on plant operation or control. Participants are invited to work with a reduced-order mechanistic model of a wastewater treatment process and to improve its predictive capabilities through the construction of a hybrid (grey-box) model. The approach combines first-principles modelling with data-driven components trained on input–output data.

The objective is to design and validate a hybrid modelling strategy—such as a parallel residual architecture—that enhances the accuracy of a reduced model while preserving its low dimensionality. The challenge highlights core mathematical issues, including model reduction, parameter identifiability, residual modelling, and validation against a high-fidelity reference simulator.

This problem emphasises model quality and approximation, rather than control performance, and illustrates how hybrid mathematical models can bridge the gap between mechanistic understanding and data-driven learning in complex wastewater treatment systems.