Neural networks for structured grid generation.

ABSTRACT: Numerical solutions of partial differential equations (PDEs) on regular domains provide simplicity as we can rely on the structure of the space. We investigate a novel neural network (NN) - based approach to generate 2-dimensional body-fitted curvilinear coordinate systems (BFCs) that allow to stay on regular grids even when the complex geometry is considered. We describe a feed-forward neural network (FNN) as a geometric transformation that can represent a diffeomorphism under certain constraints and approximations, followed by the ways of training it to create BFCs. We show that the optimization system is similar to a physics informed neural network (PINN) based solution of Winslow equations. Unlike in classical BFC generation, FNN provides a differentiable mapping between spaces, and al

SUBMITTER: Khairullin B 

PROVIDER: S-EPMC11992231 | biostudies-literature | 2025 Apr

REPOSITORIES: biostudies-literature