Preprints
https://doi.org/10.5194/gmd-2024-90
https://doi.org/10.5194/gmd-2024-90
Submitted as: development and technical paper
 | 
04 Jul 2024
Submitted as: development and technical paper |  | 04 Jul 2024
Status: a revised version of this preprint was accepted for the journal GMD and is expected to appear here in due course.

A Joint Reconstruction and Model Selection Approach for Large Scale Inverse Modeling

Malena Sabaté Landman, Julianne Chung, Jiahua Jiang, Scot Miller, and Arvind Saibaba

Abstract. Inverse models arise in various environmental applications, ranging from atmospheric modeling to geosciences. Inverse models can often incorporate predictor variables, similar to regression, to help estimate natural processes or parameters of interest from observed data. Although a large set of possible predictor variables may be included in these inverse or regression models, a core challenge is to identify a small number of predictor variables that are most informative of the model, given limited observations. This problem is typically referred to as model selection. A variety of criterion-based approaches are commonly used for model selection, but most follow a two-step process: first, select predictors using some statistical criteria, and second, solve the inverse or regression problem with these predictor variables. The first step typically requires comparing all possible combinations of candidate predictors, which quickly becomes computationally prohibitive, especially for large-scale problems. In this work, we develop a one-step approach, where model selection and the inverse model are performed in tandem. We reformulate the problem so that the selection of a small number of relevant predictor variables is achieved via a sparsity-promoting prior. Then, we describe hybrid iterative projection methods based on flexible Krylov subspace methods for efficient optimization.  These approaches are well-suited for large-scale problems with many candidate predictor variables. We evaluate our results against traditional, criteria-based approaches. We also demonstrate the applicability and potential benefits of our approach using examples from atmospheric inverse modeling based on NASA's Orbiting Carbon Observatory 2 (OCO-2) satellite.

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Malena Sabaté Landman, Julianne Chung, Jiahua Jiang, Scot Miller, and Arvind Saibaba

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gmd-2024-90', Ian Enting, 05 Aug 2024
  • RC2: 'Comment on gmd-2024-90', Anonymous Referee #2, 08 Aug 2024
  • AC1: 'Comment on gmd-2024-90: Reply to Referee 1', Julianne Chung, 25 Sep 2024
  • AC2: 'Comment on gmd-2024-90: Reply to Referee 2', Julianne Chung, 25 Sep 2024
  • AC3: 'Comment on gmd-2024-90: reply to Topic Editor', Julianne Chung, 25 Sep 2024

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gmd-2024-90', Ian Enting, 05 Aug 2024
  • RC2: 'Comment on gmd-2024-90', Anonymous Referee #2, 08 Aug 2024
  • AC1: 'Comment on gmd-2024-90: Reply to Referee 1', Julianne Chung, 25 Sep 2024
  • AC2: 'Comment on gmd-2024-90: Reply to Referee 2', Julianne Chung, 25 Sep 2024
  • AC3: 'Comment on gmd-2024-90: reply to Topic Editor', Julianne Chung, 25 Sep 2024
Malena Sabaté Landman, Julianne Chung, Jiahua Jiang, Scot Miller, and Arvind Saibaba

Model code and software

MATLAB codes for the one-dimensional deblurring example Malena Sabate Landman, Julianne Chung, Jiahua Jiang, Scot M. Miller, Arvind K. Saiababa https://zenodo.org/doi/10.5281/zenodo.11164245

Malena Sabaté Landman, Julianne Chung, Jiahua Jiang, Scot Miller, and Arvind Saibaba

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Short summary
Making an informed decision about what prior information to incorporate or discard in an inverse model is important yet very challenging, as it is often not straightforward to distinguish between informative and non-informative variables. In this study, we develop a new approach for incorporating prior information in an inverse model using predictor variables, while simultaneously selecting the relevant predictor variables for the estimation of the unknown quantity of interest.