Physics-Informed Learning Methods for Continental Waters and Marine Risks

Accurate numerical simulations of river flows, at both territorial and global scales, as well as of marine flooding, have become crucial for modern societies for multiple reasons. Floods—whether inland or coastal—and water flows at the territorial scale result from complex processes that can be described by nonlinear mathematical models based on differential equations.

Purely physics-based approaches face intrinsic limitations in representing such multi-scale (spatio-temporal) and multi-physics phenomena. In the case of watershed flows, they often rely on highly empirical parameterizations. Moreover, the computational cost of these models generally prevents their use in real-time applications.

Purely data-driven approaches may provide complementary information, but they typically require very large datasets and remain difficult to certify and interpret. Hybrid approaches that combine physics-based modeling with data-driven techniques (hybrid AI) offer a promising framework to overcome these limitations.

Principal investigators

  • Jérôme Monnier (professor INSA, IMT)
  • Olivier Roustant (professor INSA, IMT, corresponding PI)

CVs

The objective of this project is to investigate and develop hybrid AI algorithms for estimating continental-scale water flows (river networks), including extreme events such as floods and marine inundation in coastal regions.

Significant improvements are expected in terms of computational performance, predictive accuracy, and model explainability.

The research outcomes will be illustrated through case studies based on real-world scenarios. The databases employed will be multi-source, combining in situ measurements with complementary satellite observations.

The research program is structured around five interconnected axes:

  • Physics-informed learning methods: hybridization of two well-established model classes—neural networks and Gaussian processes—with physical knowledge. The resulting surrogate models and associated data assimilation strategies will be studied.
  • Reduced-basis methods: model reduction techniques based on hybrid encoders and neural network approaches.
  • Multi-fidelity models: methodologies designed to exploit hierarchies of numerical simulators with varying levels of accuracy and computational cost.
  • Uncertainty quantification: risk assessment and global sensitivity analysis aimed at improving model robustness and interpretability.
  • Design of experiments: strategies for generating new data through numerical simulations.

Co-chairs

  • Rémy Baraille (Team leader, SHOM)
  • Robin Bouclier
    (Professor, INSA-IMT, IUF Junior)
  • Pierre-André Garambois (Researcher INRAE Aix-en-Provence)
  • Josselin Garnier (Professor Ecole Polytechnique – CMAP, Académie des Sciences)
  • Nora Lüthen (Post-doc & lecturer, ETH Zürich)
  • Pascal Noble (Professor, INSA-IMT)

The chair team brings together researchers and experts from both academia and industry with complementary expertise in mathematical modeling (PDEs, probability theory, and statistics), computational sciences, scientific AI, and the relevant applied sciences (hydrology and oceanography). 

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