A Novel Hybrid Architecture Combining High-Order B-Splines and Physics-Informed Neural Networks for Solving an Astrophysical Model

In this paper, we present a novel architecture for approximating solutions to differential equations in astrophysics. Our approach introduces the innovative use of nonlinear B-spline basis functions as activation functions within a neural network. Furthermore, we develop a physics-informed B-spline neural network framework with associated control points to address the Lane--Emden equations, frequently encountered in astronomy. This new method offers enhanced accuracy while requiring fewer epochs than conventional neural networks.

کلیدواژه ها:

Physics-Informed Neural Networks ، High-Order B-Spline ، Astrophysical Modeling ، {Lane--Emden equations} ، Numerical Methods