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

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.