Artificial Intelligence for Studying Interactions of Solitons and Peakons

In this paper, Artificial Intelligence (AI) is developed for studying the Boussinesq Paradigm equation and so called b-equation based on Physics-Informed Cellular Neural Networks (PICNNs). The models studied here come from fluid dynamics. Machine learning through Physics-Informed Neural Networks (PINNs) is a powerful tool for solving complex problems arising in physical laws. By optimization and automatic differentiation, the solutions of the model under consideration can be approximated precisely and can be obtained in real time. In this paper, we shall apply a new algorithm based on Physics-Informed Cellular Neural Networks (PICNNs) for obtaining the interactions between solitons and peakons. The algorithm has many advantages, but the main ones are that it provides the fastest programming and solutions in real time. It is known that Cellular Neural Networks (CNNs) have the ability to approximate, in a very accurate way, nonlinear partial differential equations (PDEs) and to present their solutions in real time. By incorporating the physical laws into the learning process through PICNN we can solve various problems from fluid dynamics, material science, and quantum mechanics.