Applications of artificial neural networks in solving nonlinear evolution equations: wave-like and Fisher's equations

Many researchers are interested in the highly effective and successful role that deep learning techniques play in assessing many problems in various scientific disciplines. Artificial neural networks (ANNs) are considered a precise, powerful, and rapid method for the solution of ordinary differential equations and partial differential equations (PDEs). In this paper, we applied the ANN methods to solve two different types of nonlinear evolution equations: the wave-like and Fisher’s equations. We use spatial-temporal domains and the finite difference method as data-driven techniques for the suggested PDEs. We train and test the ANN using the dataset. We illustrate the graphical representation of the results to analyze the model’s accuracy. We test the model for x and t values that are different and specific. The paper illustrates the error plots where the difference is negligible, indicating that the model is well-trained and functions appropriately. We anticipate using this approach to analyze various evolution equations used in modeling diverse nonlinear phenomena that arise in different plasma models, optical fibers, and ocean waves.