Work

Bridging the Gap between Artificial Neural Networks (ANNs) and Partial Differential Equations (PDEs)

Year: 2025

Type: article

Abstract: The current research presents novel and hybrid method to tackle complex nonlinear Partial Differential Equations (PDEs) by combining Radial Basis Function Neural Networks (RBFNNs) with a powerful hybrid optimization technique. RBFNN is used to generate data from the PDEs. A hybrid Chaotic Enriched Crayfish Optimization (HCE\_CO) algorithm is utilized to optimize the RBFNN. The algorithm combines multiple optimization strategies, including Chimp Optimization Algorithms and Crayfish Optimization Algorithms. The RBFNN is trained to minimize the difference between its predictions and the actual numerical solutions by loss function. The HCE_CO algorithm adjusts the RBFNN's parameters, such as weights, biases, batch size, epochs, and number of hidden layers, to improve its accuracy. By comparing the RBFNN's predictions to numerical solutions, we found that our model achieved a Mean Absolute Error (MAE) of 7.464%, which is lower than that of previous methods.

Source: Proceedings of the Bulgarian Academy of Sciences

DOI: 10.7546/crabs.2025.04.08

Authors: Nek Muhammad, Ghulam Fatima, Khuda Amur, Emad Ismail, Fuad Awwad, Mosab Alqurashi, Abdul Hakeem

Institutions: Central South University, Xi'an University of Science and Technology, Quaid-e-Awam University of Engineering, Science and Technology, King Saud University

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4409772930

FWCI: 0.429

Cites: 3

Cited by: 1

Related to: 10