A deep artificial neural network architecture for mesh free solutions of nonlinear boundary value problems

• Published in: Applied intelligence (Dordrecht, Netherlands) Vol. 52; no. 1; pp. 916 - 926
• Main Authors: Aggarwal, Riya, Ugail, Hassan, Jha, Ravi Kumar
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2022; Springer Nature B.V
• Subjects: Accuracy; Artificial Intelligence; Artificial neural networks; Biharmonic equations; Boundary conditions; Boundary value problems; Computer architecture; Computer Science; Differential equations; Finite element method; Machines; Manufacturing; Mathematical problems; Mechanical Engineering; Neural networks; Operators (mathematics); Processes; Solid mechanics; Thin plates; Well posed problems; Biharmonic equation; Boundary value problems; Von-Kármán equation; Navier-Stokes equation; Artificial neural networks; Mesh free solutions

Seeking efficient solutions to nonlinear boundary value problems is a crucial challenge in the mathematical modelling of many physical phenomena. A well-known example of this is solving the Biharmonic equation relating to numerous problems in fluid and solid mechanics. One must note that, in general...