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

Abstract Seeking efficient solutions to nonlinear boundary value problems is a crucial challenge in the mathematical modelling of many physical phenomena. A well-known example this solving Biharmonic equation relating numerous fluid and solid mechanics. One must note that, general, it challenging solve such due higher-order partial derivatives differential operators. An artificial neural network thought be an intelligent system that learns by example. Therefore, well-posed problem can solved using system. This paper describes mesh free method based on suitably crafted deep architecture class problems. We show how suitable constructed trained satisfy associated operators conditions problem. To accuracy our method, we have tested arising from against known selected problems, e.g., comparison solution convolutional subject chosen with corresponding analytical/numerical solutions. Furthermore, demonstrate accuracy, efficiency, applicability well thin plate Navier-Stokes equation.