**Friday, 15:45 - 16:10 h, Room: H 3003A**

**Annick Sartenaer**

Derivative-free optimization for large-scale nonlinear data assimilation problems

**Coauthors: Serge Gratton, Patrick Laloyaux**

**Abstract:**

Data assimilation consists in techniques to combine observations with a numerical prediction model. The goal is to produce the best estimate of the current state of the system. Two different approaches are used in data assimilation algorithms: the sequential one, based on the statistical estimation theory (Kalman filter) and the variational one, based on the optimal control theory. This last approach amounts to solve a very large nonlinear weighted least-squares problem called 4D-Var (four-dimensional variational problem). In both approaches, evaluating derivatives is challenging as one needs to compute the Jacobian of the model operator. The Ensemble Kalman Filter (EnKF) provides a suitable derivative-free alternative for the first

approach by using a Monte-Carlo implementation on the Kalman filter equations. However, no derivative-free variant of the variational approach has been proposed so far. In this talk, we present such a variant, based on a technique to build and explore a sequence of appropriate low dimensional subspaces. Numerical illustration is shown on a shallow water data assimilation problem, including a comparison with the Ensemble Kalman Filter approach.

Talk 2 of the invited session Fri.3.H 3003A

**"Novel applications of derivative-free and simulation-based optimization"** [...]

Cluster 6

**"Derivative-free & simulation-based optimization"** [...]