the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A Joint Reconstruction and Model Selection Approach for Large Scale Inverse Modeling
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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RC1: 'Comment on gmd-2024-90', Ian Enting, 05 Aug 2024
Report on "A joint reconstruction and model selection approach for large scale inverse problems"
Ian Enting
This paper describes an inversion technique where the regularisation is based by prior predictions from models, with the new feature that
selection of an appropriate subset of models is being selected as part of the inversion.
It defines an appropriate objective function, and a new algorithm for minimising this objective function.The technique is then illustrated by three synthetic data examples, firstly a signal processing example and then two
inversions of simulated OCO-2 data.The paper is generally well written, although there are a few points at which a little more detail might make it easier to read.
It might benefit from a table of notation.To conclude, this paper is suitable for publication in Geoscientific Model Development. My various comments (in the pdf) should be regarded as suggestions for the authors to consider and the editor to take into account, rather than being prescriptive.
More detailed comments are provided in the pdf file linked to this report.
I see know need to look at any revised version.
- 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
-
RC1: 'Comment on gmd-2024-90', Ian Enting, 05 Aug 2024
Report on "A joint reconstruction and model selection approach for large scale inverse problems"
Ian Enting
This paper describes an inversion technique where the regularisation is based by prior predictions from models, with the new feature that
selection of an appropriate subset of models is being selected as part of the inversion.
It defines an appropriate objective function, and a new algorithm for minimising this objective function.The technique is then illustrated by three synthetic data examples, firstly a signal processing example and then two
inversions of simulated OCO-2 data.The paper is generally well written, although there are a few points at which a little more detail might make it easier to read.
It might benefit from a table of notation.To conclude, this paper is suitable for publication in Geoscientific Model Development. My various comments (in the pdf) should be regarded as suggestions for the authors to consider and the editor to take into account, rather than being prescriptive.
More detailed comments are provided in the pdf file linked to this report.
I see know need to look at any revised version.
- 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
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
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