Numerical Study of Dynamical System Using deep learning Approach

Abstract: This article is devoted to developing a deep learning method to the numerical solution of the partial differential equations (PDEs). Graph kernel neural networks (GKNN) approach to embedding graphs into a computationally numerical format has been used. In particular, for investigation mathematical models of the dynamical system of cancer cells invasion in inhomogeneous areas of human tissues has been considered. Neural operators were initially proposed to model the differential operator of PDEs. The GKNN mapping features between input data to the PDEs and their solutions has been constructed. The boundary integral method in combination Green's functions for a large number of boundary conditions are used. The tools applied in this development are based on the Fourier neural operators (FNOs), graph theory, theory elasticity, and singular integral equations.