Computational Mathematics and Computer Modeling with Applications (CMCMA)

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

https://doi.org/10.48308/CMCMA.5.1.1
Volume 5, Issue 1
May 2026
Pages 1-14
Computational Mathematics and Computer Modeling with Applications (CMCMA)

Document Type : Regular paper

Authors

Sima Naraghi 1
Kourosh Parand 2 ΒΆ

1 Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

2 Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

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.

Keywords

Physics-Informed Neural Networks
High-Order B-Spline
Astrophysical Modeling
{Lane--Emden equations}
Numerical Methods
  • Receive Date 30 January 2026
  • Accept Date 29 April 2026

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