-Basics tools to solve inverse problems (including examples): least-squares (linear, non-linear), regularization.
-Data Assimilation principles (variational, sequential).
– Bayesian analysis.
– Equivalences between the BLUE:Kalman filter, the MAP and VDA in the Linear-Quadratic-Gaussian case.
– A first application to model identification in experimental mechanics: (i) computation of the measures from image registration and (ii) data assimilation to calibrate constitutive laws.
-Optimal control of ODEs. Linear-Quadratic case, maximum principle, Hamiltonian.
Small practical: optimal control of a vehicle trajectory.
-Optimal control of PDEs. Gradient computation, adjoint model, optimality system.
– Variational Data Assimilation (steady-state case, unsteady case). Algorithms (3D-VAR, 4D-Var, variants).
– Examples, practical aspects.
– DA by Physics Informed Neural Networks (PINNs).
Practical (marked): estimation of river bathymetry from water surface measurements (problem arising in spatial hydrology).
Ocean circulation modelling
– Fluid mechanics at the planetary scale, Equilibrium solutions
– Shallow water equations: derivation and description of wave propagation. Applications: Gravity waves, Poincaré Waves, Kelvin Waves
-Quasi-Geostrophic equations: derivation and description of wave propagation. Applications: Rossby Waves, Gulf Stream.
