Nonlinear dynamic systems modeling using Gaussian processes: Predicting ionospheric total electron content over South Africa

Ackermann, Etienne; Villiers, J. P. de; Cilliers, Pierre J.

doi:10.1029/2010ja016375

Cited by 22 publications

(12 citation statements)

References 32 publications

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“…We give a review in Online Appendix C. We choose a Gaussian-process-based surrogate model for several reasons: (1) Gaussian processes are common for modeling uncertainty in multivariate spaces (cf. Ackermann et al, 2011;Buche et al, 2005). The underlying Gaussian distribution makes few assumptions on the actual curvature of the function.…”

Section: High-level Descriptionmentioning

confidence: 99%

Directed particle swarm optimization with Gaussian-process-based function forecasting

Jakubik¹,

Binding²,

Feuerriegel³

2021

Preprint

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Particle swarm optimization (PSO) is an iterative search method that moves a set of candidate solution around a search-space towards the best known global and local solutions with randomized step lengths. PSO frequently accelerates optimization in practical applications, where gradients are not available and function evaluations expensive. Yet the traditional PSO algorithm ignores the potential knowledge that could have been gained of the objective function from the observations by individual particles. Hence, we draw upon concepts from Bayesian optimization and introduce a stochastic surrogate model of the objective function.That is, we fit a Gaussian process to past evaluations of the objective function, forecast its shape and then adapt the particle movements based on it. Our computational experiments demonstrate that baseline implementations of PSO (i. e., SPSO2011) are outperformed. Furthermore, compared to, state-of-art surrogate-assisted evolutionary algorithms, we achieve substantial performance improvements on several popular benchmark functions. Overall, we find that our algorithm attains desirable properties for exploratory and exploitative behavior.

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Section: High-level Descriptionmentioning

confidence: 99%

Directed particle swarm optimization with Gaussian-process-based function forecasting

Jakubik¹,

Binding²,

Feuerriegel³

2021

Preprint

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“…The selected surrogate modeling method in ASDEMO is Gaussian process (GP). GP modeling is a theoretically sound and principled method for determining a much smaller number of free model parameters when compared to many other surrogate modeling approaches such as ANN [28], [29]. It can also provide an estimate of the model uncertainty for each predicted point, which is shown to have a large advantage in SAEAs [30]- [33].…”

Section: Basic Techniques a Gaussian Process Machine Learning And Prescreeningmentioning

confidence: 99%

Efficient Design Optimization of High-Performance MEMS Based on a Surrogate-Assisted Self-Adaptive Differential Evolution

et al. 2020

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High-performance microelectromechanical systems (MEMS) are playing a critical role in modern engineering systems. Due to computationally expensive numerical analysis and stringent design specifications nowadays, both the optimization efficiency and quality of design solutions become challenges for available MEMS shape optimization methods. In this paper, a new method, called self-adaptive surrogate model-assisted differential evolution for MEMS optimization (ASDEMO), is presented to address these challenges. The main innovation of ASDEMO is a hybrid differential evolution mutation strategy combination and its self-adaptive adoption mechanism, which are proposed for online surrogate model-assisted MEMS optimization. The performance of ASDEMO is demonstrated by a high-performance electro-thermoelastic micro-actuator, a high-performance corrugated membrane micro-actuator, and a highly multimodal mathematical benchmark problem. Comparisons with state-of-the-art methods verify the advantages of ASDEMO in terms of efficiency and optimization ability.INDEX TERMS MEMS design optimization, high-performance MEMS design, surrogate model assisted evolutionary algorithm, Gaussian process, differential evolution.

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“…Another GPR approach was used to predict daily TEC values based upon the TEC values recorded at various permanent GNSS station in Turkey Inyurt et al (2020). A comparison of Gaussian process (GP) and neural network model was performed by Ackermann et al (2011) over a test area in South Africa. The GP framework presented many advantages over competing modeling strategies, such as providing powerful and convenient ways of incorporating prior knowledge and requiring less training data than neural networks.…”

Section: Introductionmentioning

confidence: 99%

Gauss process regression for real-time ionospheric delay estimation from GNSS observations

Lupsic

Takács

2022

Acta Geod Geophys

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The number of devices equipped with global satellite positioning has exceeded seven billion recently. There are a wide variety of receivers regarding their accuracy and reliability. Low cost, multi-frequency units have been released on the market latterly; however, the number of single-frequency receivers is still significant. Since their measurements are influenced by ionospheric delay, accurate ionosphere models are of utmost importance to reduce the effect. This paper summarizes how Gauss process regression (GPR) can be applied to derive near real-time regional ionosphere models using raw Global Navigation Satellite System (GNSS) observations of permanent stations. While Gauss process is widely used in machine learning, GPR is a nonparametric, Bayesian approach to regression. GPR has several benefits for ionosphere monitoring since it is quite robust and efficient to derive a grid model from data available in irregular set of ionospheric pierce points. The corresponding instrumental delays are estimated by a parallel Kalman filter. The presented algorithm can be applied near real-time, however the results are offline calculated and are compared to two high quality TEC map products. Based on the analysis, the accuracy of the GPR modell is in 2 TECu range. The developed methods could be efficiently applied in the field of autonomous vehicle navigation with meeting both accuracy and integrity requirements.

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Nonlinear dynamic systems modeling using Gaussian processes: Predicting ionospheric total electron content over South Africa

Cited by 22 publications

References 32 publications

Directed particle swarm optimization with Gaussian-process-based function forecasting

Directed particle swarm optimization with Gaussian-process-based function forecasting

Efficient Design Optimization of High-Performance MEMS Based on a Surrogate-Assisted Self-Adaptive Differential Evolution

Gauss process regression for real-time ionospheric delay estimation from GNSS observations

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