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Full-Text Articles in Other Physical Sciences and Mathematics
Solution Of Fractional Order Diffusion Equations With Clique Neural Network, Merve Zeynep Kaya, Mesut Karabacak, Ercan Çelik
Solution Of Fractional Order Diffusion Equations With Clique Neural Network, Merve Zeynep Kaya, Mesut Karabacak, Ercan Çelik
Mathematical Modelling and Numerical Simulation with Applications
In this paper, the clique artificial neural network method is used to solve the fractional diffusion equation, which is a subclass of partial differential equations. The clique neural network architecture is constructed using input, hidden, and output layers. Several degrees of clique polynomials were used as activation functions, and the output layer was obtained by multiplying them with weight coefficients. Subsequently, the optimization equation was derived, and the exact solution, numerical solution, and error function graphs were obtained using a specialized algorithm. Analysis of the results demonstrates that the clique artificial neural network method provides quicker and more accurate results …
Convolution And Autoencoders Applied To Nonlinear Differential Equations, Noah Borquaye
Convolution And Autoencoders Applied To Nonlinear Differential Equations, Noah Borquaye
Electronic Theses and Dissertations
Autoencoders, a type of artificial neural network, have gained recognition by researchers in various fields, especially machine learning due to their vast applications in data representations from inputs. Recently researchers have explored the possibility to extend the application of autoencoders to solve nonlinear differential equations. Algorithms and methods employed in an autoencoder framework include sparse identification of nonlinear dynamics (SINDy), dynamic mode decomposition (DMD), Koopman operator theory and singular value decomposition (SVD). These approaches use matrix multiplication to represent linear transformation. However, machine learning algorithms often use convolution to represent linear transformations. In our work, we modify these approaches to …
Development Of A Technological Modeling System For Refining Processes, Isomiddin Siddikov, Akmal Ganiev
Development Of A Technological Modeling System For Refining Processes, Isomiddin Siddikov, Akmal Ganiev
Bulletin of TUIT: Management and Communication Technologies
The article considers with the creation of a modeling system that allows the formation the dynamics of the technological process. Taking into account its physical and chemical properties. To solve this issue, the application of a semantic network is proposed, which ensures the aggregation of process models based on their compatibility. The proposed approach is implemented for dehydrogenation parameters, which showed the effectiveness of the proposed approach.