Offre en lien avec l’Action/le Réseau : EXMIA/Doctorants

Laboratoire/Entreprise : Laboratoire de Génie Chimique (LGC)
Durée : 3 ans
Contact : rachid.ouaret@toulouse-inp.fr
Date limite de publication : 2026-04-10

Contexte :
In France, more than 22,000 wastewater treatment plants collect and treat approximately 8.4 billion
m3 of wastewater annually, but less than 1% of this treated water is currently reused. In response
to recent drought episodes and the increasing scarcity of water resources, the “Water plan (Plan
Eau)” was introduced in 2023 to promote a more resilient and concerted management of water
resources, including the valorization of treated wastewater reuse (REUT) [1]. Membrane bioreactors (MBRs) are recognized wastewater treatment processes known for their excellent purification
performance and are now deployed in large-scale installations. However, these systems consume
at least twice the energy of conventional activated sludge systems (CAS), primarily due to their
high aeration requirements [3, 4]. This energy demand is further influenced by the concentration
of Total Suspended Solids (TSS), which directly affects reactor volume and design. Addressing
these issues requires advanced mathematical models capable of optimizing MBR performance while
accounting for uncertainties in influent characteristics, operational conditions, effluent quality, and
energy efficiency.
The scientific complexity of this issue lies in the intrinsically nested nature of MBR models. Unlike
traditional approaches that consider systems as “single-block” entities, large-scale MBRs involve
a deeply nested structure where the output of one sub-model (biological, physical, or energetic)
becomes the input of another [2]. This specific architecture generates complex multi-scale and
multi-frequency dynamics. Biological phenomena directly influence the production of suspended
solids and EPS (Extracellular Polymeric Substances), which condition membrane fouling, creating
a strongly coupled physico-biological system with multiple feedback loops. This nested structure
is essential for faithfully capturing the real behavior of industrial installations, but it considerably
complicates the analysis and management of uncertainties.
The uncertainties present in these systems are multiple and dependent: they concern the influent
(flow rate, COD, NH+
4
, TSS), operational conditions (control parameters), and membrane fouling.
These uncertainties evolve over time, are described by heterogeneous data often asynchronous or
incomplete, and exhibit complex structural dependencies that cannot be captured by classical statistical methods. In particular, dependencies between variables (linear or nonlinear, symmetric or
asymmetric) require specific tools such as copulas for precise modeling [5]. This complexity of uncertainties is exacerbated by the nature of the collected data: wastewater treatment plants generate
time series at different temporal scales (from seconds to weeks), with distinct time steps between
online sensors, laboratory analyses, and operational histories.
Sensitivity analysis represents an essential lever for understanding and optimizing these systems, but
it faces major challenges in the context of nested models. Traditional sensitivity analysis methods,
developed for single-block models, do not allow for fine analysis of sub-model contributions nor
correct quantification of sensitivities in a nested structure [6]. A specific approach is therefore
necessary to evaluate how variations in input parameters affect final outputs through the entire
modeling chain. This sensitivity analysis must also integrate symbolic data representation (intervals,
histograms, empirical distributions) to capture uncertainty without resorting to temporal smoothing
that would lose critical information [7].

Sujet :
The heart of this PhD lies in the development of an innovative methodology articulating nested
modeling, sensitivity analysis, and artificial intelligence for large-scale membrane bioreactors. This
approach builds upon preliminary work conducted at LGC on integrated MBR modeling [8, 9] and
leverages promising results recently obtained in the field of sensitivity analysis of hybrid models
[10, 11].
Nested modeling constitutes the foundation of this PhD. Unlike traditional single-block approaches, we will develop a graphical representation of interdependencies between biological (ASM-SMP),
physical (RIS), and energetic sub-models, following an approach similar to that proposed by Touboul
[12]. This nested structure will enable faithful capture of multiple feedback loops between different MBR system components, particularly between biological pollutant degradation processes and
physical membrane filtration phenomena. The use of probabilistic tools such as copulas [13] will
allow rigorous modeling of stochastic dependencies between influential variables, while a variant of
the Total Interaction Index (TII) [14] will be implemented to assess stochastic dependencies within
the nested framework.
Sensitivity analysis occupies a central position in this PhD, with the objective of developing sensitivity measures specifically adapted to nested and multi-scale structures. We will deploy classical
tools well-documented in specialized literature (derivative-based, distribution-based, or variogrambased approaches) [15], while conducting an in-depth reflection on the specificity of nested model
structures to tailor these tools to our specific context. The Shapley effect for sensitivity analysis
with dependent inputs [16, 13] will also be considered within the framework of this project, offering an innovative perspective for quantifying individual and joint contributions of parameters in a
dependency context.
Artificial intelligence will play a complementary and essential role in this PhD, particularly through
the development of Physics-Informed Neural Networks (PINN) and machine learning model interpretability techniques. This hybrid approach, which combines the advantages of mechanistic models
and data-driven methods, has already proven its worth in the field of process engineering [18] and
specifically for wastewater treatment [19]. Recent work by Danesh et al. [17, 11] has demonstrated
the effectiveness of model-agnostic methods (Accumulated Local Effects, Partial Dependence Plots)
for making neural network predictions interpretable, a fundamental requirement for the adoption
of these tools by industrial operators.
Reinforcement learning (RL) will constitute the third pillar of this PhD, with the objective of developing a real-time control framework for optimizing MBR operations. Building upon the nested
models developed and sensitivity analyses performed, this RL framework will dynamically adjust
operational parameters based on process variability. State estimation techniques, such as the Extended Kalman Filter (EKF), will be implemented to enhance RL decision-making by mitigating
measurement noise and handling system uncertainties [20, 21]. The integration of RL with mechanistic models will ensure that the control strategy remains explainable and applicable to real-world
operations

Profil du candidat :
Education: Master’s degree or equivalent (5 years) in applied mathematics, statistics, process engineering, control engineering, data science, or related field.

Formation et compétences requises :
Technical skills:
– Probability and statistics (sensitivity analysis, stochastic processes)
– Dynamical systems modeling and differential equations
– Optimization and optimal control
– Machine learning and reinforcement learning
– Scientific programming (Python, R, MATLAB, Julia)
• Assets: Knowledge in process engineering or water treatment would be a plus
• Personal qualities: Autonomy, scientific rigor, taste for interdisciplinary research
• Languages: Scientific English (reading, writing, oral communication)

Adresse d’emploi :
4 allée Emile Monso
CS 84234
31 432 Toulouse cedex 4

Document attaché : 202603101043_ANR_FlexMIEE_Offre_these_fr_en.pdf