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  • Open Access

    ARTICLE

    Incorporating Lasso Regression to Physics-Informed Neural Network for Inverse PDE Problem

    Meng Ma1,2,*, Liu Fu1,2, Xu Guo3, Zhi Zhai1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 385-399, 2024, DOI:10.32604/cmes.2024.052585 - 20 August 2024

    Abstract Partial Differential Equation (PDE) is among the most fundamental tools employed to model dynamic systems. Existing PDE modeling methods are typically derived from established knowledge and known phenomena, which are time-consuming and labor-intensive. Recently, discovering governing PDEs from collected actual data via Physics Informed Neural Networks (PINNs) provides a more efficient way to analyze fresh dynamic systems and establish PED models. This study proposes Sequentially Threshold Least Squares-Lasso (STLasso), a module constructed by incorporating Lasso regression into the Sequentially Threshold Least Squares (STLS) algorithm, which can complete sparse regression of PDE coefficients with the constraints More >

  • Open Access

    ARTICLE

    Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

    Rania Saadah1, Mohammed Amleh1, Ahmad Qazza1, Shrideh Al-Omari2,*, Ahmet Ocak Akdemir3

    CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1593-1616, 2024, DOI:10.32604/cmes.2023.029180 - 17 November 2023

    Abstract In this study, we aim to investigate certain triple integral transform and its application to a class of partial differential equations. We discuss various properties of the new transform including inversion, linearity, existence, scaling and shifting, etc. Then, we derive several results enfolding partial derivatives and establish a multi-convolution theorem. Further, we apply the aforementioned transform to some classical functions and many types of partial differential equations involving heat equations, wave equations, Laplace equations, and Poisson equations as well. Moreover, we draw some figures to illustrate 3-D contour plots for exact solutions of some selected More >

  • Open Access

    ARTICLE

    On Time Fractional Partial Differential Equations and Their Solution by Certain Formable Transform Decomposition Method

    Rania Saadeh1, Ahmad Qazza1, Aliaa Burqan1, Shrideh Al-Omari2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 3121-3139, 2023, DOI:10.32604/cmes.2023.026313 - 09 March 2023

    Abstract This paper aims to investigate a new efficient method for solving time fractional partial differential equations. In this orientation, a reliable formable transform decomposition method has been designed and developed, which is a novel combination of the formable integral transform and the decomposition method. Basically, certain accurate solutions for time-fractional partial differential equations have been presented. The method under concern demands more simple calculations and fewer efforts compared to the existing methods. Besides, the posed formable transform decomposition method has been utilized to yield a series solution for given fractional partial differential equations. Moreover, several More >

  • Open Access

    ARTICLE

    The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

    Fairouz Tchier1, Hassan Khan2,3,*, Shahbaz Khan2, Poom Kumam4,5, Ioannis Dassios6

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2137-2153, 2023, DOI:10.32604/cmes.2023.022855 - 23 November 2022

    Abstract The nonlinearity in many problems occurs because of the complexity of the given physical phenomena. The present paper investigates the non-linear fractional partial differential equations’ solutions using the Caputo operator with Laplace residual power series method. It is found that the present technique has a direct and simple implementation to solve the targeted problems. The comparison of the obtained solutions has been done with actual solutions to the problems. The fractional-order solutions are presented and considered to be the focal point of this research article. The results of the proposed technique are highly accurate and More >

  • Open Access

    ARTICLE

    A Weighted Average Finite Difference Scheme for the Numerical Solution of Stochastic Parabolic Partial Differential Equations

    Dumitru Baleanu1,2,3, Mehran Namjoo4, Ali Mohebbian4, Amin Jajarmi5,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1147-1163, 2023, DOI:10.32604/cmes.2022.022403 - 27 October 2022

    Abstract In the present paper, the numerical solution of Itô type stochastic parabolic equation with a time white noise process is imparted based on a stochastic finite difference scheme. At the beginning, an implicit stochastic finite difference scheme is presented for this equation. Some mathematical analyses of the scheme are then discussed. Lastly, to ascertain the efficacy and accuracy of the suggested technique, the numerical results are discussed and compared with the exact solution. More >

  • Open Access

    ARTICLE

    Cherenkov Radiation: A Stochastic Differential Model Driven by Brownian Motions

    Qingqing Li1,2, Zhiwen Duan1,2,*, Dandan Yang1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 155-168, 2023, DOI:10.32604/cmes.2022.019249 - 29 September 2022

    Abstract With the development of molecular imaging, Cherenkov optical imaging technology has been widely concerned. Most studies regard the partial boundary flux as a stochastic variable and reconstruct images based on the steadystate diffusion equation. In this paper, time-variable will be considered and the Cherenkov radiation emission process will be regarded as a stochastic process. Based on the original steady-state diffusion equation, we first propose a stochastic partial differential equation model. The numerical solution to the stochastic partial differential model is carried out by using the finite element method. When the time resolution is high enough, More >

  • Open Access

    ARTICLE

    The Fractional Investigation of Fornberg-Whitham Equation Using an Efficient Technique

    Hassan Khan1,2, Poom Kumam3,4,*, Asif Nawaz1, Qasim Khan1, Shahbaz Khan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 259-273, 2023, DOI:10.32604/cmes.2022.021332 - 29 September 2022

    Abstract In the last few decades, it has become increasingly clear that fractional calculus always plays a very significant role in various branches of applied sciences. For this reason, fractional partial differential equations (FPDEs) are of more importance to model the different physical processes in nature more accurately. Therefore, the analytical or numerical solutions to these problems are taken into serious consideration and several techniques or algorithms have been developed for their solution. In the current work, the idea of fractional calculus has been used, and fractional Fornberg Whitham equation (FFWE) is represented in its fractional More >

  • Open Access

    ARTICLE

    On Fuzzy Conformable Double Laplace Transform with Applications to Partial Differential Equations

    Thabet Abdeljawad1,2, Awais Younus3,*, Manar A. Alqudah4, Usama Atta5

    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 2163-2191, 2023, DOI:10.32604/cmes.2022.020915 - 20 September 2022

    Abstract The Laplace transformation is a very important integral transform, and it is extensively used in solving ordinary differential equations, partial differential equations, and several types of integro-differential equations. Our purpose in this study is to introduce the notion of fuzzy double Laplace transform, fuzzy conformable double Laplace transform (FCDLT). We discuss some basic properties of FCDLT. We obtain the solutions of fuzzy partial differential equations (both one-dimensional and two-dimensional cases) through the double Laplace approach. We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations. More >

  • Open Access

    ARTICLE

    LaNets: Hybrid Lagrange Neural Networks for Solving Partial Differential Equations

    Ying Li1, Longxiang Xu1, Fangjun Mei1, Shihui Ying2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.1, pp. 657-672, 2023, DOI:10.32604/cmes.2022.021277 - 24 August 2022

    Abstract We propose new hybrid Lagrange neural networks called LaNets to predict the numerical solutions of partial differential equations. That is, we embed Lagrange interpolation and small sample learning into deep neural network frameworks. Concretely, we first perform Lagrange interpolation in front of the deep feedforward neural network. The Lagrange basis function has a neat structure and a strong expression ability, which is suitable to be a preprocessing tool for pre-fitting and feature extraction. Second, we introduce small sample learning into training, which is beneficial to guide the model to be corrected quickly. Taking advantages of More >

  • Open Access

    ARTICLE

    Breakdown Voltage Prediction by Utilizing the Behavior of Natural Ester for Transformer Applications

    P. Samuel Pakianathan*, R. V. Maheswari

    Intelligent Automation & Soft Computing, Vol.35, No.3, pp. 2717-2736, 2023, DOI:10.32604/iasc.2023.029950 - 17 August 2022

    Abstract This research investigates the dielectric performance of Natural Ester (NE) using the Partial Differential Equation (PDE) tool and analyzes dielectric performance using fuzzy logic. NE nowadays is found to replace Mineral Oil (MO) due to its extensive dielectric properties. Here, the heat-tolerant Natural Esters Olive oil (NE1), Sunflower oil (NE2), and Ricebran oil (NE3) are subjected to High Voltage AC (HVAC) under different electrodes configurations. The breakdown voltage and leakage current of NE1, NE2, and NE3 under Point-Point (P-P), Sphere-Sphere (S-S), Plane-Plane (PL-PL), and Rod-Rod (R-R) are measured, and survival probability is presented. The electric… More >

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