21 Nov 2022
21 Nov 2022
Status: this preprint is open for discussion.

An Adjoint-Free Algorithm for CNOPs via Sampling

Bin Shi1,3 and Guodong Sun2,3 Bin Shi and Guodong Sun
  • 1State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • 2State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
  • 3University of Chinese Academy of Sciences, Beijing 100049, China

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.

Bin Shi and Guodong Sun

Status: open (until 16 Jan 2023)

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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.