Neural networks catching up with finite differences in solving partial differential equations in higher dimensions
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DOI: 10.1007/s00521-020-04743-8
Abstract: Solving partial differential equations using neural networks is mostly a proof of concept approach. In the case of direct function approximation, a single neural network is constructed to be the solution of a particular boundary… read more here.
Keywords: partial differential; neural networks; finite differences; solution ... See more keywords
ANN-based methods for solving partial differential equations: a survey
Sign Up to like & getrecommendations! Published in 2022 at "Arab Journal of Basic and Applied Sciences"
DOI: 10.1080/25765299.2022.2104224
Abstract: Abstract Traditionally, partial differential equation (PDE) problems are solved numerically through a discretization process. Iterative methods are then used to determine the algebraic system generated by this process. Recently, scientists have emerged artificial neural networks… read more here.
Keywords: ann based; methods solving; partial differential; based methods ... See more keywords
Solving Partial Differential Equations Using Deep Learning and Physical Constraints
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DOI: 10.3390/app10175917
Abstract: The various studies of partial differential equations (PDEs) are hot topics of mathematical research. Among them, solving PDEs is a very important and difficult task. Since many partial differential equations do not have analytical solutions,… read more here.
Keywords: equations using; using deep; partial differential; deep learning ... See more keywords