This project explores the development and application of Physics-Informed Neural Networks (PINNs) to solve complex differential equations governing physical systems. By integrating known physical laws (e.g., conservation laws, PDEs) directly into the neural network’s loss function, PINNs leverage both data-driven learning and physics-based constraints, enabling accurate predictions even with sparse or noisy data. The study focuses on optimizing PINN architectures, training strategies, and hybrid approaches to improve convergence and generalization across domains such as fluid dynamics, heat transfer, and structural mechanics. Through numerical experiments and benchmark comparisons, the project aims to demonstrate PINNs’ effectiveness in solving forward and inverse problems while reducing reliance on high-fidelity simulations. Key challenges, such as handling multi-scale phenomena and improving training efficiency, will also be investigated to advance the adoption of PINNs in scientific and engineering applications.