Solution of Allen - Cahn equation Using Physics - Informed Neural Networks

Physics-informed neural network integrates the physical properties of a structure through the border cost constraint within the loss property of the neural network. The methodology has demonstrated significant efficacy in estimating the relationship among the outcome of a PDE and its spatiotemporal variables. A unique PINN technique is presented by successively solving the PDE across multiple consecutive sections with only one neural network. The primary concept is to undergo rebuilding the identical neural network to address the PDE across consecutive duration intervals, during adhering to the previously acquired solutions across all prior time segment. The benefits of PINN are demonstrated by the resolution of the Allen-Cahn formulas. These formulas are extensively employed to characterise distinction of phases and reaction-diffusion processes. Novel approaches have been suggested to enhance the suggested PINN scheme. The strategy employs a transfer learning methodology that retains the characteristics acquired from prior training. This research demonstrates that this method considerably enhances the reliability and efficacy of the PINN scheme.