Levenberg-Marquardt’s and Gauss-Newton algorithms for parameter optimisation of the motion of a point mass rolling on a turntable

Haddout, Soufiane; Rhazi, M.

doi:10.1080/17797179.2016.1191120

Cited by 7 publications

(4 citation statements)

References 20 publications

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“…This could be used to solve the parameter estimation problem for compartmental models such as the SIR and SEIR models. Basically, the LM algorithm is the combination of the gradient descent method and Gauss-Newton method (Haddout and Rhazi, 2015). The LM method acts more like a gradient-descent method when the parameters are far from their optimal value, and becomes more like the Gauss-Newton one when the parameters are close to the optimal value.…”

Section: /17mentioning

confidence: 99%

Peer Review #1 of "Assessing the effects of time-dependent restrictions and control actions to flatten the curve of COVID-19 in Kazakhstan (v0.1)"

2021

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This paper presents the assessment of time-dependent national-level restrictions and control actions and their effects in fighting the COVID-19 pandemic. By analysing the transmission dynamics during the first wave of COVID-19 in the country, the effectiveness of the various levels of control actions taken to flatten the curve can be better quantified and understood. This in turn can help the relevant authorities to better plan for and control the subsequent waves of the pandemic. To achieve this, a deterministic population model for the pandemic is firstly developed to take into consideration the time-dependent characteristics of the model parameters, especially on the ever-evolving value of the reproduction number, which is one of the critical measures used to describe the transmission dynamics of this pandemic. The reproduction number alongside other key parameters of the model can then be estimated by fitting the model to real-world data using numerical optimisation techniques or by inducing ad-hoc control actions as recorded in the news platforms. In this paper, the model is verified using a case study based on the data from the first wave of COVID-19 in the Republic of Kazakhstan. The model is fitted to provide estimates for two settings in simulations; time-invariant and time-varying (with bounded constraints) parameters. Finally, some forecasts are made using four scenarios with time-dependent control measures so as to determine which would reflect on the actual situations better.

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Section: /17mentioning

confidence: 99%

Peer Review #1 of "Assessing the effects of time-dependent restrictions and control actions to flatten the curve of COVID-19 in Kazakhstan (v0.1)"

2021

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“…Thus, Under the BDregular condition, they prove that PSA-LMM is locally superlinearly convergent, for semi-smooth equations and locally quadratically convergent for strongly semi-smooth equations. In [4], Haddout and Rhazi try solving the problem of non-linear least squares, based upon LM and Gauss-Newton methods by minimizing the sum of squares of errors between the data and model prediction.…”

Section: Related Workmentioning

confidence: 99%

Applying Bayesian Regularization for Acceleration of Levenberg Marquardt based Neural Network Training

Suliman¹,

Omarov²

2018

IJIMAI

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Neural network is widely used for image classification problems, and is proven to be effective with high successful rate. However one of its main challenges is the significant amount of time it takes to train the network. The goal of this research is to improve the neural network training algorithms and apply and test them in classification and recognition problems. In this paper, we describe a method of applying Bayesian regularization to improve Levenberg-Marquardt (LM) algorithm and make it better usable in training neural networks. In the experimental part, we qualify the modified LM algorithm using Bayesian regularization and use it to determine an appropriate number of hidden layers in the network to avoid overtraining. The result of the experiment was very encouraging with a 98.8% correct classification when run on test samples.

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“…This could be used to solve the parameter estimation problem for compartmental models such as the SIR and SEIR models. Basically, the LM algorithm is the combination of the gradient descent method and Gauss–Newton method ( Haddout & Rhazi, 2015 ). The LM method acts more like a gradient-descent method when the parameters are far from their optimal value, and becomes more like the Gauss–Newton one when the parameters are close to the optimal value.…”

Section: Introductionmentioning

confidence: 99%

Assessing the effects of time-dependent restrictions and control actions to flatten the curve of COVID-19 in Kazakhstan

Duc

Gui

2021

PeerJ

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This article presents the assessment of time-dependent national-level restrictions and control actions and their effects in fighting the COVID-19 pandemic. By analysing the transmission dynamics during the first wave of COVID-19 in the country, the effectiveness of the various levels of control actions taken to flatten the curve can be better quantified and understood. This in turn can help the relevant authorities to better plan for and control the subsequent waves of the pandemic. To achieve this, a deterministic population model for the pandemic is firstly developed to take into consideration the time-dependent characteristics of the model parameters, especially on the ever-evolving value of the reproduction number, which is one of the critical measures used to describe the transmission dynamics of this pandemic. The reproduction number alongside other key parameters of the model can then be estimated by fitting the model to real-world data using numerical optimisation techniques or by inducing ad-hoc control actions as recorded in the news platforms. In this article, the model is verified using a case study based on the data from the first wave of COVID-19 in the Republic of Kazakhstan. The model is fitted to provide estimates for two settings in simulations; time-invariant and time-varying (with bounded constraints) parameters. Finally, some forecasts are made using four scenarios with time-dependent control measures so as to determine which would reflect on the actual situations better.

show abstract

Levenberg-Marquardt’s and Gauss-Newton algorithms for parameter optimisation of the motion of a point mass rolling on a turntable

Cited by 7 publications

References 20 publications

Peer Review #1 of "Assessing the effects of time-dependent restrictions and control actions to flatten the curve of COVID-19 in Kazakhstan (v0.1)"

Peer Review #1 of "Assessing the effects of time-dependent restrictions and control actions to flatten the curve of COVID-19 in Kazakhstan (v0.1)"

Applying Bayesian Regularization for Acceleration of Levenberg Marquardt based Neural Network Training

Assessing the effects of time-dependent restrictions and control actions to flatten the curve of COVID-19 in Kazakhstan

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