MathHydroNum denotes a French multidisciplinary team offering expertise in numerical hydrology and the software platform DassHydro (Data Assimilation in Hydrology) dedicated to numerical modeling of surface hydrodynamics and hydrology.

The team brings together expertise in computational sciences, hydrology, hydraulics, mathematical models and methods, inverse problems, statistical inference, sensitivity analysis, data assimilation, reduced models, and physically informed neural networks.

The objectives of MathHydroNum are to design models, numerical methods, algorithms, and computational softwares that address scientific challenges in the following areas:

  • Spatial hydrology, both at the global scale and regional scales, based on spatial observations (CNES, ESA, NASA etc missions),
  • Numerical simulations of floods and inundations.

Current research areas

  • Multi-scale flexible hydrological-hydraulic modeling.
  • Multi-source data assimilation.
  • Model reduction in hydraulics and hydrology.
  • Hybrid physically-informed neural networks.
  • Hybrid deterministic stochastic data assimilation algorithms.

Algorithmic products

  • Numerical models for flood propagation at the watershed scale.
  • River discharge estimation at both planetary and regional scales.
  • Rivers bathymetry profiles estimation.
  • Hydrology-hydraulics models coupling.
  • Non-linear rheology parameters estimation.

Computational software: DassHydro

DassHydro includes DassFlow and SMASH softwares.
These codes rely on shared technologies : MPI Fortran kernels, Python wrapping, data assimilation processes, ML processes.
These codes are available on GitHub.


The various developments of DassFlow have been co-funded by INSA Toulouse since 2008, by CNRS in the 2010s, by INSA Strasbourg in 2015-2020, by CNES since 2014, by INRAe Aix since 2020, and by the French agency ANR (Muffins project, 2022-25).


The various developments of SMASH have been co-funded by INRAe and the national flood forecasting center SCHAPI-DGPR since 2017, by the French agency ANR (Muffins project, 2022-25) and European agency DG-ECHO.