14 Ensemble Kalman filter for neural network-based one-shot inversion
Philipp A. Guth, Claudia Schillings, Simon Weißmann · 2022
We study the use of novel techniques arising in machine learning for inverse problems. Our approach replaces the complex forward model by a neural network, which is trained simultaneously in a one-shot sense when estimating the unknown parameters from data, i. e., the neural network is trained only for the unknown parameter. By establishing a link to the Bayesian approach to inverse problems we develop an algorithmic framework that ensures the feasibility of the parameter estimate with respect to the forward model. We propose an efficient, derivative-free optimization method based on variants of the ensemble Kalman inversion. Numerical experiments show that the ensemble Kalman filter for neural network-based one-shot inversion is a promising direction combining optimization and machine learning techniques for inverse problems.