Adaptive Levenberg–Marquardt Algorithm: A New Optimization Strategy for Levenberg–Marquardt Neural Networks

Yan, Zhiqi; Zhong, Shisheng; Lin, Lin; Cui, Zhiquan

doi:10.3390/math9172176

Cited by 26 publications

(9 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This typically resulted in fitting errors during the first 1–2 min of anodization ( h PAAO < 200 nm) as shown in Figure 3a . Moreover, the LM algorithm is sensitive to the initial guess value of the fit parameters and may converge to a bad local minimum [ 33 ] resulting in a wrong thickness value.…”

Section: Resultsmentioning

confidence: 99%

In situ optical sub-wavelength thickness control of porous anodic aluminum oxide

Dutovs,

Popļausks,

Putāns

et al. 2024

Beilstein J. Nanotechnol.

View full text Add to dashboard Cite

Porous anodic aluminum oxide (PAAO), sometimes referred to as nanoporous anodic alumina, serves as a cost-effective template for nanofabrication in many fields of science and engineering. However, production of ultrathin PAAO membranes with precise thickness in the optical sub-wavelength range remains challenging because of difficulties regarding process control at the initial stage of anodic oxidation. In this study, we demonstrate a technique for consistently manufacturing PAAO with the targeted thickness. An electrochemical cell with an optical window was designed for reflectance spectroscopy of PAAO during anodization. Real-time fitting of spectra to a transfer-matrix model enabled continuous monitoring of the thickness growth of the PAAO layer. Automation software was designed to terminate the anodization process at preset PAAO thickness values. While the concept was illustrated using the widely used method of anodization in a 0.3 M oxalic acid electrolyte with a 40 V potential, it can be readily customized for other protocols. PAAO layers with effective thickness below 300 nm could be produced with a few nanometers accuracy using single-crystal aluminum substrates. The results were confirmed using spectroscopic ellipsometry. The method for controlling the thickness during anodization eliminates the necessity of sample sectioning for electron microscopy and is particularly valuable for the small-scale production of PAAO-based functional optical coatings.

show abstract

Section: Resultsmentioning

confidence: 99%

In situ optical sub-wavelength thickness control of porous anodic aluminum oxide

Dutovs,

Popļausks,

Putāns

et al. 2024

Beilstein J. Nanotechnol.

View full text Add to dashboard Cite

show abstract

“…The weights and biases are adjusted to minimize the MSE of the training dataset only. The neural network is implemented in the MATLAB version 2023.1 deep learning toolbox [19] in agreement to the Levenberg-Marquardt algorithm [20,21]. The algorithm is used many times, each of them referred to as an epoch) on the training dataset, measuring the MSE for each training, validation, and testing set.…”

Section: Neural Network Definition and Trainingmentioning

confidence: 99%

Computing Interface Curvature from Height Functions using Machine Learning with a Symmetry-preserving Approach for Two-phase Simulations

Cervone,

Manservisi,

Scardovelli

et al. 2024

Preprint

View full text Add to dashboard Cite

The volume of fluid (VOF) method is a popular technique for the direct numerical simulations of flows involving immiscible fluids. A discrete volume fraction field evolving in time represents the interface, in particular, to compute its geometric properties. The height function method (HF) is based on the volume fraction field, and its estimate of the interface curvature converges with second-order accuracy with grid refinement. Data-driven methods have been recently proposed as an alternative to computing the curvature, with particular consideration for a well-balanced input data set generation and symmetry preservation. In the present work, a two-layer feed-forward neural network is trained on an input data set generated from the height function data instead of the volume fraction field. The symmetries for rotations, reflections, and the anti-symmetry for the phase swapping have been considered to reduce the number of input parameters. The neural network, establishing a correlation between curvature and height function values, can efficiently predict the local interface curvature. We compare the trained neural network to the standard Height Function method to assess its performance and robustness.

show abstract

“…Trust-region algorithms provide more robustness compared to line-search methods. The SCG based training algorithm addresses the drawback of the line-search method by incorporating the trust-region method, similar to the approach utilized in the Levenberg-Marquardt method [47].…”

Section: Scaled Conjugate Gradient (Scg) Based Training Algorithmmentioning

confidence: 99%

Scaled Conjugate Gradient Neural Intelligence for Motion Parameters Prediction of Markov Chain Underwater Maneuvering Target

Ali,

Zuberi,

Qing

et al. 2024

JMSE

View full text Add to dashboard Cite

This study proposes a novel application of neural computing based on deep learning for the real-time prediction of motion parameters for underwater maneuvering object. The intelligent strategy utilizes the capabilities of Scaled Conjugate Gradient Neural Intelligence (SCGNI) to estimate the dynamics of underwater target that adhere to discrete-time Markov chain. Following a state-space methodology in which target dynamics are combined with noisy passive bearings, nonlinear probabilistic computational algorithms are frequently used for motion parameters prediction applications in underwater acoustics. The precision and robustness of SCGNI are examined here for effective motion parameter prediction of a highly dynamic Markov chain underwater passive vehicle. For investigating the effectiveness of the soft computing strategy, a steady supervised maneuvering route of undersea passive object is designed. In the framework of bearings-only tracking technology, system modeling for parameters prediction is built, and the effectiveness of the SCGNI is examined in ideal and cluttered marine atmospheres simultaneously. The real-time location, velocity, and turn rate of dynamic target are analyzed for five distinct scenarios by varying the standard deviation of white Gaussian observed noise in the context of mean square error (MSE) between real and estimated values. For the given motion parameters prediction problem, sufficient Monte Carlo simulation results support SCGNI’s superiority over typical generalized pseudo-Bayesian filtering strategies such as Interacting Multiple Model Extended Kalman Filter (IMMEKF) and Interacting Multiple Model Unscented Kalman Filter (IMMUKF).

show abstract

Adaptive Levenberg–Marquardt Algorithm: A New Optimization Strategy for Levenberg–Marquardt Neural Networks

Cited by 26 publications

References 24 publications

In situ optical sub-wavelength thickness control of porous anodic aluminum oxide

In situ optical sub-wavelength thickness control of porous anodic aluminum oxide

Computing Interface Curvature from Height Functions using Machine Learning with a Symmetry-preserving Approach for Two-phase Simulations

Scaled Conjugate Gradient Neural Intelligence for Motion Parameters Prediction of Markov Chain Underwater Maneuvering Target

Contact Info

Product

Resources

About