From Newton to Neural Networks: A Review of Data-Driven Physical Modelling and the Rise of Physics-Informed AI

Abstract

This review examines the evolution of physical modelling from classical first-principles approaches to contemporary data-driven and physics-informed learning frameworks. It begins with the historical foundations of scientific modelling, including classical mechanics, field equations, computational simulation, and statistical mechanics, and shows how these traditions established differential equations and numerical methods as core tools in science and engineering. The review then discusses the rise of data-driven modelling, covering statistical learning, machine learning, deep learning, and Gaussian processes, with attention to their strengths in handling complex nonlinear systems and their limitations in interpretability, data requirements, and physical consistency. A central focus is placed on Physics-Informed Neural Networks (PINNs) and related hybrid methods that integrate governing laws into learning algorithms to improve prediction, generalization, and physical plausibility. Applications across fluid dynamics, structural engineering, climate science, biomedicine, materials discovery, and energy systems are highlighted. Finally, the review identifies key challenges related to scalability, uncertainty quantification, robustness, and benchmarking, and outlines future directions such as active learning, operator learning, and scientific foundation models.