Abstract
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.
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