Empirical Evaluation of Bayesian Optimization in Parametric Tuning of Chaotic Systems

Abbas, Mudassar; Ilin, Alexander; Solonen, Antti; Hakkarainen, Janne; Oja, Erkki; Järvinen, Heikki

doi:10.1615/int.j.uncertaintyquantification.2016016645

Cited by 3 publications

(3 citation statements)

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“…GBO is widely used in the tech-industry and in engineering, and, to a lesser extent, in the Earth sciences. The use of GBO for parameter and state estimation problems was pioneered by Abbas et al (2016) and we continue this line of work by discussing the use of GBO in ensemble data assimilation (DA), where the goal is to estimate a model's state based on noisy observations. We specifically discussed three related problems in ensemble DA and how these can be tackled by GBO: i. parameter estimation problems in which some, or all, of the parameters that define the model used in the ensemble DA are uncertain or unknown; ii.…”

Section: Discussionmentioning

confidence: 99%

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Using global Bayesian optimization in ensemble data assimilation: parameter estimation, tuning localization and inflation, or all of the above

Lunderman

Morzfeld

Posselt

2021

Tellus A: Dynamic Meteorology and Oceanography

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Global Bayesian optimization (GBO) is a derivative-free optimization method that is used widely in the techindustry to optimize objective functions that are expensive to evaluate, numerically or otherwise. We discuss the use of GBO in ensemble data assimilation (DA), where the goal is to update the state of a numerical model in view of noisy observations. Specifically, we consider three tasks: (i) the estimation of model parameters; (ii) the tuning of localization and inflation in ensemble DA; (iii) doing both, i.e. estimating model parameters while simultaneously tuning the localization and inflation of the ensemble DA. For all three tasks, the GBO works 'offline', i.e. a set of 'training' observations are used within GBO to determine appropriate model or localization/inflation parameters, which are subsequently deployed within an ensemble DA system. Because of the offline nature of the technique, GBO can easily be combined with existing DA systems and it can effectively decouple (nearly) linear/Gaussian aspects of a problem from highly nonlinear/ non-Gaussian ones. We illustrate the use of GBO in simple numerical experiments with the classical Lorenz problems. Our main goals are to introduce GBO in the context of ensemble DA and to spark an interest in GBO and its uses for streamlining important tasks in ensemble DA.

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Section: Discussionmentioning

confidence: 99%

“…An example of the use of GBO in a geophysical problem is the recent work of Pirot et al (2019), where GBO is used for underground contaminant source localization. A second example is the work of Abbas et al (2016), which leverages GBO in the context of simultaneous state and parameter estimation problems.…”

Section: Introductionmentioning

confidence: 99%

Using global Bayesian optimization in ensemble data assimilation: parameter estimation, tuning localization and inflation, or all of the above

Lunderman

Morzfeld

Posselt

2021

Tellus A: Dynamic Meteorology and Oceanography

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“…This optimisation is performed by the well-known multi-objective metaheuristic NSGA-II (non sorting genetic algorithm-II) [19]. Bayesian optimisation has been used once on chaotic dynamics: Abbas et al [20] tune parameters of a chaotic system (Lorenz 95) to underline the capabilities of Bayesian optimisation method on complex system. Indeed Bayesian optimisation has been successfully employed to optimise Machine Learning parameters [21] and multi-level optimisation problems [22].…”

Section: Metaheuristics For Chaotic Dynamicsmentioning

confidence: 99%

Bayesian optimisation to select Rössler system parameters used in Chaotic Ant Colony Optimisation for Coverage

Rosalie

Kieffer

Brust

et al. 2020

Journal of Computational Science

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The CACOC (Chaotic Ant Colony optimisation for Coverage) algorithm has been developed to manage the mobility of a swarm of Unmanned Aerial Vehicles (UAVs). Using a specific chaotic dynamic obtained from the Rössler system, CACOC provides waypoints for UAVs that aim to optimise the coverage of an unknown area while having unpredictable trajectories. Since the chaotic dynamics are obtained from a three differential equations system with parameters, it is possible to tune one parameter to obtain another chaotic dynamic, which will result in different UAV mobility behaviours. This work aims at optimising this parameter of the Rössler chaotic system to improve the coverage performance of CACOC. Since each evaluation of a solution requires a full simulation, global optimisation techniques (e.g., population-based heuristics) would be very time-consuming. We therefore considered a surrogate-based method to efficiently explore the parameter space of the Rössler system for CACOC, i.e., Bayesian optimisation. Experimental results demonstrate that this approach permits to improve the speed of coverage of the UAV swarm. In addition an analysis of the dynamical properties of the obtained chaotic system is provided.

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Perspectives on the integration between first-principles and data-driven modeling

Bradley

Kim

Kilwein

et al. 2022

Computers & Chemical Engineering

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Empirical Evaluation of Bayesian Optimization in Parametric Tuning of Chaotic Systems

Cited by 3 publications

References 0 publications

Using global Bayesian optimization in ensemble data assimilation: parameter estimation, tuning localization and inflation, or all of the above

Using global Bayesian optimization in ensemble data assimilation: parameter estimation, tuning localization and inflation, or all of the above

Bayesian optimisation to select Rössler system parameters used in Chaotic Ant Colony Optimisation for Coverage

Perspectives on the integration between first-principles and data-driven modeling

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