Physics-informed neural networks (PINNs) represent a significant advancement at the intersection of machine learning and physical sciences, offering a powerful framework for solving complex problems governed by physical laws. This survey provides a comprehensive review of the current state of research on PINNs, highlighting their unique methodologies, applications, challenges, and future directions. The paper begins by introducing the fundamental concepts underlying neural networks and the motivation for integrating physics-based constraints. It then explores various PINN architectures and techniques for incorporating physical laws into neural network training, including approaches to solving partial differential equations (PDEs) and ordinary differential equations (ODEs). Additionally, the paper discusses the primary challenges faced in developing and applying PINNs, such as computational complexity, data scarcity, and the integration of complex physical laws. The applications of PINNs are reviewed across diverse fields, including fluid dynamics, material science, quantum mechanics, and geophysics. These applications demonstrate the versatility and effectiveness of PINNs in addressing complex scientific and engineering problems. The paper also identifies promising future research directions, including algorithmic techniques, interdisciplinary collaborations, scalability, and addressing robustness issues. Overall, this survey seeks to provide a foundational understanding of PINNs within this rapidly evolving field, highlighting their potential to bridge the gap between machine learning and physical sciences, and to enhance the accuracy, robustness, and interpretability of models in various scientific and engineering contexts.Physics-informed neural networks (PINNs) represent a significant advancement at the intersection of machine learning and physical sciences, offering a powerful framework for solving complex problems governed by physical laws. This survey provides a comprehensive review of the current state of research on PINNs, highlighting their unique methodologies, applications, challenges, and future directions. The paper begins by introducing the fundamental concepts underlying neural networks and the motivation for integrating physics-based constraints. It then explores various PINN architectures and techniques for incorporating physical laws into neural network training, including approaches to solving partial differential equations (PDEs) and ordinary differential equations (ODEs). Additionally, the paper discusses the primary challenges faced in developing and applying PINNs, such as computational complexity, data scarcity, and the integration of complex physical laws. The applications of PINNs are reviewed across diverse fields, including fluid dynamics, material science, quantum mechanics, and geophysics. These applications demonstrate the versatility and effectiveness of PINNs in addressing complex scientific and engineering problems. The paper also identifies promising future research directions, including algorithmic techniques, interdisciplinary collaborations, scalability, and addressing robustness issues. Overall, this survey seeks to provide a foundational understanding of PINNs within this rapidly evolving field, highlighting their potential to bridge the gap between machine learning and physical sciences, and to enhance the accuracy, robustness, and interpretability of models in various scientific and engineering contexts.