a Novel Discrete Optimal Transport Method for Bayesian Inverse Problems
Abstract
We present the Augmented Ensemble Transform (AET) method for generating approximate samples from a high-dimensional posterior distribution as a solution to Bayesian inverse problems. Solving large-scale inverse problems is critical for some of the most relevant and impactful scientific endeavors of our time. Therefore, constructing novel methods for solving the Bayesian inverse problem in more computationally efficient ways can have a profound impact on the science community. This research derives the novel AET method for exploring a posterior by solving a sequence of linear programming problems, resulting in a series of transport maps which map prior samples to posterior samples, allowing for the computation of moments of the posterior. We show both theoretical and numerical results, indicating this method can offer superior computational efficiency when compared to other SMC methods. Most of this efficiency is derived from matrix scaling methods to solve the linear programming problem and derivative-free optimization for particle movement. We use this method to determine inter-well connectivity in a reservoir and the associated uncertainty related to certain parameters. The attached file shows the difference between the true parameter and the AET parameter in an example 3D reservoir problem. The error is within the Morozov discrepancy allowance with lower computational cost than other particle methods.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2017
- Bibcode:
- 2017AGUFMNG23A..08B
- Keywords:
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- 3315 Data assimilation;
- ATMOSPHERIC PROCESSES;
- 1910 Data assimilation;
- integration and fusion;
- INFORMATICS;
- 3260 Inverse theory;
- MATHEMATICAL GEOPHYSICS;
- 4468 Probability distributions;
- heavy and fat-tailed;
- NONLINEAR GEOPHYSICS