The Ensemble Kalman Filter for Dynamic Inverse Problems

Simon Weissmann; Neil K. Chada; Xin T. Tong

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arXiv · 2401.11948

The Ensemble Kalman Filter for Dynamic Inverse Problems

Simon Weissmann·Neil K. Chada·Xin T. Tong

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Abstract

In inverse problems, the goal is to estimate unknown model parameters from noisy observational data. Traditionally, inverse problems are solved under the assumption of a fixed forward operator describing the observation model. In this article, we consider the extension of this approach to situations where we have a dynamic forward model, motivated by applications in scientific computation and engineering. We specifically consider this extension for a derivative-free optimizer, the ensemble Kalman inversion (EKI). We introduce and justify a new methodology called dynamic-EKI, which is a particle-based method with a changing forward operator. We analyze our new method, presenting results related to the control of our particle system through its covariance structure. This analysis includes moment bounds and an ensemble collapse, which are essential for demonstrating a convergence result. We establish convergence in expectation and validate our theoretical findings through experiments with dynamic-EKI applied to a 2D Darcy flow partial differential equation.

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Simon Weissmann, Neil K. Chada, Xin T. Tong. 2024-01-22. The Ensemble Kalman Filter for Dynamic Inverse Problems. https://arxiv.org/abs/2401.11948

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