Filtering methods for coupled inverse problems

TL;DR

This paper introduces an ensemble Kalman method with a weighted function approach for solving multi-objective inverse problems, providing explicit weight updates and demonstrating improved performance through numerical examples.

Contribution

The paper presents a novel ensemble Kalman method with explicit weight update formulas for coupled inverse problems, enhancing solution accuracy.

Findings

Improved performance demonstrated in numerical experiments

Explicit weight update formula derived from mean field analysis

Effective for multi-objective inverse problems

Abstract

We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem 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.