Ensemble Kalman filter for neural network based one-shot inversion

05/05/2020
by   Philipp A. Guth, et al.
0

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, an algorithmic framework is developed which ensures the feasibility of the parameter estimate w.r. 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.

READ FULL TEXT
research
08/02/2019

On the Incorporation of Box-Constraints for Ensemble Kalman Inversion

The Bayesian approach to inverse problems is widely used in practice to ...
research
12/15/2018

Adding Constraints to Bayesian Inverse Problems

Using observation data to estimate unknown parameters in computational m...
research
03/18/2020

Data-Driven Forward Discretizations for Bayesian Inversion

This paper suggests a framework for the learning of discretizations of e...
research
07/26/2022

A Review of the EnKF for Parameter Estimation

The ensemble Kalman filter is a well-known and celebrated data assimilat...
research
07/15/2023

Gradient-free training of neural ODEs for system identification and control using ensemble Kalman inversion

Ensemble Kalman inversion (EKI) is a sequential Monte Carlo method used ...
research
09/20/2023

Flow Annealed Kalman Inversion for Gradient-Free Inference in Bayesian Inverse Problems

For many scientific inverse problems we are required to evaluate an expe...
research
08/10/2018

Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks

The standard probabilistic perspective on machine learning gives rise to...

Please sign up or login with your details

Forgot password? Click here to reset