Numerical solutions of wavelet neural networks for fractional differential equations

Wu, Mingqiu; Zhang, Jinlei; Huang, Zhijie; Li, Xiang; Yang, Dong

doi:10.1002/mma.7449

Cited by 12 publications

(5 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Tan et al [6] investigated solutions of PDE using an unsupervised WNN model with meta-heuristic algorithm. Wu et al [27] proposed a WNN with the structure 1×N×1 to find the numerical solution of fractional differential equations. These literatures stimulate the authors to investigate different wavelet kernels as an alternative, reliable, efficient, and robust computing paradigm for solving non-linear phenomena of the oceanographic WMR model.…”

Section: Related Studiesmentioning

confidence: 99%

Modeling of Mexican Hat Wavelet Neural Network with L-BFGS Algorithm for Simulating the Recycling Procedure of Waste Plastic in Ocean

Sahoo¹,

Chakraverty²

2023

JEMSE

View full text Add to dashboard Cite

In the global economy, plastics are considered a versatile and ubiquitous material. It can reach to marine ecosystems through diverse channels, such as road runoff, wastewater pathways, and improper waste management. Therefore, rapid mitigation and reduction are required for this ever-growing problem. The marine habitats are believed to be the highest emitters and absorbers of O2 and CO2 respectively. As such, every day, the prominence of managing the litter in the ocean is growing effectively and efficiently. One of the most significant challenges in oceanography is creating a comprehensive meshless algorithm to handle the mathematical representation of waste plastic management in the ocean. This research dedicates to studying the dynamics of waste plastic management model governed by a mathematical representation depending on three components viz. Waste plastic (W), Marine litter (M) and Recycling of debris (R), i.e., WMR model. In this regard, an unsupervised machine learning approach, namely Mexican Hat Wavelet Neural Network (MhWNN) refined by the efficient Limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm (L-BFGS), i.e., MhWNN-LBFGS model has been implemented for handling the non-linear phenomena of WMR models. Besides, the obtained solution is meshfree and compared with the state-of-art numerical result to establish the precision of the MhWNN-LBFGS model. Furthermore, different global statistical measures (MAPE, TIC, RMSE, and ENSE) have been computed at twenty testing points to validate the stability of the proposed algorithm.

show abstract

Section: Related Studiesmentioning

confidence: 99%

Modeling of Mexican Hat Wavelet Neural Network with L-BFGS Algorithm for Simulating the Recycling Procedure of Waste Plastic in Ocean

Sahoo¹,

Chakraverty²

2023

JEMSE

View full text Add to dashboard Cite

show abstract

“…Several techniques are utilized to solve the different FDEs. For example, the wavelet approach is followed in [4]. The approach of operational matrices is followed in various papers; see, for example, [5,6].…”

Section: Introductionmentioning

confidence: 99%

A computational strategy for nonlinear time-fractional generalized Kawahara equation using new eighth-kind Chebyshev operational matrices

Ahmed,

Hafez,

Abd-Elhameed

2024

Phys. Scr.

View full text Add to dashboard Cite

This paper uses a new method to numerically solve the nonlinear time-fractional generalized Kawahara equations (NTFGKE) with uniform initial boundary conditions (IBCs). A class of modified shifted eighth-kind Chebyshev polynomials (MSEKCPs) is defined to satisfy the given IBCs. The proposed method is based on using operational matrices (OMs) for the ordinary derivatives (ODs) and fractional derivatives (FDs) of MSEKCPs. These OMs are employed together with the spectral collocation method (SCM). Our presented algorithm enables the extraction of efficient and accurate numerical solutions. The convergence of the suggested method and the error analysis have been developed. Three numerical examples are presented to demonstrate the applicability and accuracy of our algorithm. Some comparisons of the presented numerical results with other existing ones are offered to validate the efficiency and superiority of our approach. Tables and graphs demonstrate that the proposed approach produces approximate solutions with high accuracy.

show abstract

“…Furthermore, a wavelet neural network was proposed to get the fractional differential equations solution in Ref. [28]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

An Artificial Neural Network Approach for Solving Space Fractional Differential Equations

Dai

Yu²

2022

Symmetry

View full text Add to dashboard Cite

The linear algebraic system generated by the discretization of fractional differential equations has asymmetry, and the numerical solution of this kind of problems is more complex than that of symmetric problems due to the nonlocality of fractional order operators. In this paper, we propose the artificial neural network (ANN) algorithm to approximate the solutions of the fractional differential equations (FDEs). First, we apply truncated series expansion terms to replace unknown function in equations, then we use the neural network to get series coefficients, and the obtained series solution can make the norm value of loss function reach a satisfactory error. In the part of numerical experiments, the results verify that the proposed ANN algorithm can make the numerical results achieve high accuracy and good stability.

show abstract

Numerical solutions of wavelet neural networks for fractional differential equations

Cited by 12 publications

References 25 publications

Modeling of Mexican Hat Wavelet Neural Network with L-BFGS Algorithm for Simulating the Recycling Procedure of Waste Plastic in Ocean

Modeling of Mexican Hat Wavelet Neural Network with L-BFGS Algorithm for Simulating the Recycling Procedure of Waste Plastic in Ocean

A computational strategy for nonlinear time-fractional generalized Kawahara equation using new eighth-kind Chebyshev operational matrices

An Artificial Neural Network Approach for Solving Space Fractional Differential Equations

Contact Info

Product

Resources

About