Physics Informed Deep Learning Approach for Differential Equation

Abstract

This study presents a Physics-Informed Neural Network (PINN) approach for solving differential equations, providing a versatile and data-driven alternative to traditional methods. Focusing on the comparison between exact, analytic, and neural network solutions, we investigate the effectiveness of PINNs in capturing complex dynamics across diverse applications. The comparison is illustrated through carefully crafted graphs, highlighting the accuracy and efficiency of the PINN methodology. By eliminating the need for explicit analytical solutions, PINNs offer a flexible framework for addressing a wide range of differential equations, showcasing their potential to revolutionize problem-solving in various scientific and engineering domains. This research contributes valuable insights into the capabilities of PINNs and their role in advancing computational methodologies for differential equations.