An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling

In this paper, we propose a sampling algorithm based on state-of-the-art statistical machine learning techniques to obtain conditional nonlinear optimal perturbations (CNOPs), which is different from traditional (deterministic) optimization methods.1 Specifically, the traditional approach is unavail...

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Bibliographic Details
Published in:Nonlinear processes in geophysics Vol. 30; no. 3; pp. 263 - 276
Main Authors: Shi, Bin, Sun, Guodong
Format: Journal Article
Language:English
Published: Gottingen Copernicus GmbH 06.07.2023
Copernicus Publications
Subjects:
Algorithms
Analysis
Atmosphere
Atmospheric models
Burgers equation
Computation
Computing time
Fluid dynamics
General circulation models
Machine learning
Mathematical models
Methods
Modelling
Numerical models
Objective function
Ocean models
Optimization
Ordinary differential equations
Perturbation
Perturbations
Probability theory
Sampling
Viscosity
ISSN:1607-7946, 1023-5809, 1607-7946
Online Access:Get full text
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Summary:In this paper, we propose a sampling algorithm based on state-of-the-art statistical machine learning techniques to obtain conditional nonlinear optimal perturbations (CNOPs), which is different from traditional (deterministic) optimization methods.1 Specifically, the traditional approach is unavailable in practice, which requires numerically computing the gradient (first-order information) such that the computation cost is expensive, since it needs a large number of times to run numerical models. However, the sampling approach directly reduces the gradient to the objective function value (zeroth-order information), which also avoids using the adjoint technique that is unusable for many atmosphere and ocean models and requires large amounts of storage. We show an intuitive analysis for the sampling algorithm from the law of large numbers and further present a Chernoff-type concentration inequality to rigorously characterize the degree to which the sample average probabilistically approximates the exact gradient. The experiments are implemented to obtain the CNOPs for two numerical models, the Burgers equation with small viscosity and the Lorenz-96 model. We demonstrate the CNOPs obtained with their spatial patterns, objective values, computation times, and nonlinear error growth. Compared with the performance of the three approaches, all the characters for quantifying the CNOPs are nearly consistent, while the computation time using the sampling approach with fewer samples is much shorter. In other words, the new sampling algorithm shortens the computation time to the utmost at the cost of losing little accuracy.
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ISSN:1607-7946
1023-5809
1607-7946
DOI:10.5194/npg-30-263-2023