Filtering Methods for Coupled Inverse Problems

In many applications it is required to determine a parameters set which is suitable for competing models. To this end, we are interested in ensemble methods to solve multiobjective optimization problems. Here, the ensemble Kalman Filter method is applied and adapted in order to solve coupled inverse nonlinear problems using a weighted function approach. An analysis of the mean field limit of the ensemble method yields an explicit update formula for the weights. Numerical examples show the improved performance of the proposed method.