Evaluating Single Multiplicative Neuron Models In Physics-informed Neural Networks For Differential Equations

This article discusses the challenges and problems that can arise during the design and training of artificial neural networks (ANNs), such as overfitting, underfitting, and imbalanced data. It also introduces the concept of the Self-Modifying Neural Network Model (SMNM) and its potential application in solving differential equations within the framework of Physics-Informed Neural Networks (PINNs). However, the implementation of SMNM within PINNs did not converge, leading to the development of a new strategy called the mimic SMNM model. This revised model aims to combine the theoretical advantages of SMNM with practical applicability and improved computational speed.