Preprints
https://doi.org/10.5194/egusphere-2022-1268
https://doi.org/10.5194/egusphere-2022-1268
21 Nov 2022
 | 21 Nov 2022

An Adjoint-Free Algorithm for CNOPs via Sampling

Bin Shi and Guodong Sun

Abstract. In this paper, we propose a sampling algorithm based on statistical machine learning to obtain conditional nonlinear optimal perturbation (CNOP), which is different from traditional deterministic optimization methods. The new approach reduces the expensive gradient (first-order) information directly by the objective value (zeroth-order) information and does not use the adjoint technique that requires large amounts of storage and produces instability due to linearization. An intuitive analysis of the sampling algorithm is shown rigorously within the form of a concentration inequality for the approximate gradient. The numerical experiments of a theoretical model, Burgers equation with small viscosity, are implemented to obtain the CNOPs. The performance of standard spatial structures demonstrates that at the cost of losing accuracy, the sample-based method with fewer samples spends time relatively shorter than the adjoint-based method and directly from the definition. Finally, we show that the nonlinear time evolution of the CNOPs obtained by all the algorithms is nearly consistent with the quantity of norm square of perturbations, their difference and relative difference based on the definition method.

Journal article(s) based on this preprint

06 Jul 2023
An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling
Bin Shi and Guodong Sun
Nonlin. Processes Geophys., 30, 263–276, https://doi.org/10.5194/npg-30-263-2023,https://doi.org/10.5194/npg-30-263-2023, 2023
Short summary

Bin Shi and Guodong Sun

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload
AR by Bin Shi on behalf of the Authors (15 Feb 2023)  Author's response   Author's tracked changes   Manuscript 
ED: Referee Nomination & Report Request started (16 Feb 2023) by Stefano Pierini
RR by Anonymous Referee #1 (28 Feb 2023)
RR by Anonymous Referee #3 (04 Apr 2023)
ED: Reconsider after major revisions (further review by editor and referees) (05 Apr 2023) by Stefano Pierini
AR by Bin Shi on behalf of the Authors (10 May 2023)  Author's response   Author's tracked changes   Manuscript 
ED: Referee Nomination & Report Request started (14 May 2023) by Stefano Pierini
RR by Anonymous Referee #3 (01 Jun 2023)
ED: Publish as is (04 Jun 2023) by Stefano Pierini
AR by Bin Shi on behalf of the Authors (05 Jun 2023)  Author's response   Manuscript 

Journal article(s) based on this preprint

06 Jul 2023
An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling
Bin Shi and Guodong Sun
Nonlin. Processes Geophys., 30, 263–276, https://doi.org/10.5194/npg-30-263-2023,https://doi.org/10.5194/npg-30-263-2023, 2023
Short summary

Bin Shi and Guodong Sun

Bin Shi and Guodong Sun

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Short summary
In this paper, we introduced a sample-based algorithm to obtain the CNOPs. Compared with the classical adjoint-based method, this approach is easier to implement and reduces the required storage for the basic state. When we reduce the number of samples to some extent, it reduces the computation markedly more when using the sample-based method, which can guarantee that the CNOP obtained is nearly consistent with some minor fluctuating errors oscillating in spatial distribution.