## Invited Session Fri.3.H 3003A

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

**Cluster 6: Derivative-free & simulation-based optimization** [...]

### Novel applications of derivative-free and simulation-based optimization

**Chair: Luís Nunes Vicente and Stefan Wild**

**Friday, 15:15 - 15:40 h, Room: H 3003A, Talk 1**

**Juan Meza**

Derivative-free optimization methods for determining the surface structure of nanosystems

**Abstract:**

Many properties of nanosystems depend on the atomic configuration at the surface. One common technique used for determining this surface structure is based on the low energy electron diffraction (LEED) method, which uses a sophisticated physics model to compute the diffraction spectra. While this approach is highly effective, the computational cost of the simulations can be prohibitive for large systems. Here, we describe the use of pattern search methods and simplified physics surrogates for determining the surface structure of nanosystems. The pattern search methods have the property of being able to handle both continuous and categorical variables. This allows the simultaneous optimization of the atomic coordinates as well as the chemical identity.

**Friday, 15:45 - 16:10 h, Room: H 3003A, Talk 2**

**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.

**Friday, 16:15 - 16:40 h, Room: H 3003A, Talk 3**

**Andrew R. Conn**

Simulation-based optimization: Integrating seismic and production data in history matching

**Coauthors: Sippe Douma, Lior Horesh, Eduardo Jimenez, Gijs van Essen**

**Abstract:**

We present two recent complementary approaches to mitigate the ill-posedness of this problem: Joint inversion - the development of a virtual sensing formulation for efficient and consistent assimilation of 4D time-lapse seismic data; Flow relevant geostatistical sampling - despite conscientious efforts to minimize the undeterminedness of the solution space, through joint inversion or through regularization, the distribution of the unknown parameters conditional on the historical data, often remains illusive. This is typically accounted for through extensive sampling. We propose a reduced space hierarchical clustering of flow-relevant indicators for determining representatives of these samples. This allows us to identifying model characteristics that affect the dynamics.

The effectiveness of both methods are demonstrated both with synthetic and real field data.

Time permitting we will discuss the ramifications for the optimization and the numerical linear algebra.