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Full-Text Articles in Education
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 …
Application Of Evolutionary Network Concept In Structuring Mathematics Curriculum, Aditi Mitra
Application Of Evolutionary Network Concept In Structuring Mathematics Curriculum, Aditi Mitra
Electronic Theses and Dissertations
Phylogenetic tree and in general, evolutionary network, has found its application well beyond the biological fields and has even percolated into recent high demanding areas, such as data mining and social media chain reactions. An extensive survey of its current applications are presented here. An attempt has been made to apply the very concept in the mathematics course curriculum inside a degree program. Various features of the tree structure are identified within the curriculum network. To highlight various key components and to enhance the visual effect, several diagrams are presented. The combined effect of these diagram provides a sense of …