A Novel Approach for Approximating the Dynamics of Fisher's Equation Based on Physics-Informed Neural Networks

The precise and efficient interpretation of Fisher's equation is paramount while comprehending different dynamics of biological population spread and colonization. In this context, Physics-informed neural networks (PINNs) are emerging as a promising alternative to conventional numerical methods. This paper highlights the distinct advantages of using PINN in solving Fisher's equations compared to traditional methods. This method involves numerically approximated partial differential equations through PINNs based on the sampling of Latin supermassives. The optimization was performed using Adam's optimization technique to minimize the root mean square loss function associated with the targeted partial differential equation. This study provides a powerful tool that not only accurately predicts population distribution, but also captures underlying dynamics of the system. The effectiveness of the mentioned method is highlighted with numerous numerical testing and comparative analysis with traditional numerical methods.