This paper explores the transformative impact of Artificial Intelligence (AI) and Machine Learning (ML) in engineering, emphasizing their integration with computational science to address complex challenges and optimize infrastructure. By leveraging advanced neural network architectures, such as Physics-Informed Neural Networks (PINNs) and deep learning models, AI facilitates efficient simulations, predictive maintenance, and generative design, significantly reducing computational demands while ensuring physical validity. The role of digital twins, augmented by AR/VR technologies, is highlighted in enabling real-time monitoring, decision-making, and urban planning innovations. Reinforcement learning is presented as a key tool in adaptive traffic signal control, showcasing the potential of AI in smart city applications. Case studies demonstrate practical implementations, such as predicting concrete compressive strength, optimizing beam deflection, and enabling structural health monitoring using neural networks. Despite these advancements, challenges related to data quality, model interpretability, and legacy system integration persist, requiring interdisciplinary collaboration and hybrid frameworks for sustainable innovation. Future directions emphasize the integration of quantum computing, scalable AI tools, and distributed computing frameworks to enhance engineering workflows and foster the development of resilient, efficient, and adaptive systems.