NEURAL NETWORK-DRIVEN ADAPTIVE ROOT-FINDING ALGORITHM: LEARNING TO SOLVE NONLINEAR EQUATIONS MORE EFFICIENTLY

2025/07/24 by Aghamie, Sunday O., Ehiwario, Jacob, Eboh, Godday
#Algorithm #Bisection method #Neural Network #Newton-Raphson method #Secant method #machine learning

paper · doi:10.60787/jnamp.vol69no2.526

Abstract

Root-finding methods such as Bisection, Newton-Raphson, and Secant are classical algorithms for solving nonlinear equations. This study proposes an adaptive classification-based approach using a neural network to predict the best method based on initial iteration behavior. The model achieves up to 100% classification accuracy. Results are validated with training/test loss trends, classification reports, and confusion matrices, and benchmarked against classical numerical analyse.

Related

• Root finding techniques that work
• A Neural-Operator Preconditioned Newton Method for Accelerated Nonlinear Solvers
• Adaptive Physics-informed Neural Networks: A Survey
• Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy
• Gradient-Free Learning Based on the Kernel and the Range Space