SOLVING SOME NON LINEAR PDES INVERSE PROBLEMS USING VARIATIONAL DATA ASSIMILATION

We present a practical technique for calculating adjoint codes arising in variational methods for data assimilation. Our aim is to bring a more to the automatic differentiation in the MatLab langage. It is used to identify the initial condition of the problem governed by a non linear partial differential equation. The cost function gradient’s is derived by using the discrete adjoint model. Numerical examples are presented for Kardar-Parisi-Zhang equation using explicit Euler discretisation in time and pseudo-spectral discretisation in the 2D space dimension. The numerical results obtained from the MatLab environment allow us to verify the efficient of this scheme.