Background and Scientific Issues:

Combined sewer systems are under increasing pressure due to urbanization, soil sealing, and the intensification of extreme precipitation events driven by climate change. These trends are increasing the frequency and intensity of discharges of untreated wastewater into the natural environment, with major environmental, public health, and regulatory consequences. In heavily urbanized areas, existing infrastructure has limited hydraulic capacity, making this issue particularly critical. Nature-based solutions (swales, rain gardens, green roofs, retention/infiltration basins) offer promising ways to reduce runoff volumes and limit overflows. However, their effectiveness depends heavily on local hydrological characteristics, their spatial distribution, and future climate conditions. Despite the ability of machine learning methods to identify factors influencing overflows (Alwosheel et al., 2018; Montoya-Coronado et al., 2024; Kratzert et al., 2019), these approaches remain limited by: (a) the lack of explicit consideration of the physical laws governing hydrological processes; (b) their low robustness in the face of hydroclimatic non-stationarity; and (c) 

insufficient quantification of the uncertainties associated with climate projections and their propagation in predictive models. Furthermore, existing approaches rely primarily on historical precipitation records, which are not very representative of future conditions. A major scientific challenge therefore lies in developing models capable of producing physically consistent predictions that are robust to climate uncertainties and directly applicable to decision-making in urban hydrology.
Consequently, the scientific problem is as follows: “How can we develop a Physics-Informed Machine Learning (PIML) framework capable of predicting future overflows in combined sewer systems under climate change, identifying priority areas for intervention, and optimizing stormwater management strategies at the source, while quantifying the associated uncertainties?”

Scientific Objectives and Methodology:

The main objective is to develop an innovative methodological framework combining physics-informed machine learning, hydrological modeling, and future climate scenarios to improve the prediction and management of overflows. The specific objectives are:
1.    Develop a hydrologically consistent PIML model. Design a hybrid model that explicitly integrates conservation laws (mass, mechanical energy) and conceptual hydrological representations (model 

(reservoir models, rainfall-runoff transformation functions, infiltration processes). The preferred approach will be based on differentiable neural networks coupled with physical modules (of the “differentiable modeling” type, Tsai et al., 2021), with physical constraints integrated into the cost function.
2.    Assess robustness under climate change. Integrate regional climate projections (EURO-CORDEX, CMIP6; SSP2-4.5 and SSP5-8.5 scenarios) after bias correction and statistical downscaling to evaluate the model’s predictive capability under non-stationary hydroclimatic conditions.
3.    Identify critical areas and optimize solutions. Couple the PIML model with a distributed hydrological model to locate the sub-basins that contribute most to overflows and evaluate the effectiveness of various stormwater disconnection strategies (infiltration, retention, evapotranspiration, and de-impermeabilization).
4.    Quantify and propagate uncertainties. Develop a probabilistic framework (climate ensembles, parameter sensitivity analysis, Bayesian estimation) to propagate uncertainties from climate projections to operational recommendations.

The methodology consists of four steps:

1.    Creation and structuring of the database. Compilation and structuring of historical and future precipitation data, flow and water level measurements from monitoring networks, GIS data, land use data, green infrastructure inventories, and existing hydrological and hydraulic simulations for the pilot site(s).
2.    Development of the Physics-Informed Machine Learning model. Design of a hybrid architecture combining supervised learning and physical constraints. Hydrological laws will be integrated via penalties in the cost functions and differentiable physical modules. Performance will be evaluated through systematic comparison with purely data-driven models (LSTM, Random Forest) and purely physical models, using metrics of accuracy, temporal generalization, and physical consistency.
3.    Hydrological coupling and prospective simulations. Simulation of climate change impacts using multi-scenario ensembles to assess spill volumes and frequencies, sensitivity to climate uncertainties, and the robustness of source-based management strategies.
4.    Operational application. Application in the instrumented pilot area of Écully (69), then, once the methodological approach has been validated in this watershed, it will be applied to other regions (Milan, Italy, or Quebec, Canada) to test the general applicability of the tools developed in contrasting climatic contexts; the objective is to produce vulnerability maps, land-use scenarios, and decision-support indicators that incorporate probabilistic indicators for local governments. The expected results will contribute to the development of a digital twin of urban water management systems, capable of assisting managers in planning infrastructure that is resilient to climate change.