From Mathematical Modeling and Simulation to Digital Twins: Bridging Theory and Digital Realities in Industry and Emerging Technologies

Abstract

Against the background of the unprecedented advancements related to Industry 4.0 and beyond, transitioning from classical mathematical models to fully embodied digital twins represents a critical change in the planning, monitoring, and optimization of complex industrial systems. This work outlines the subject within the broader field of applied mathematics and computational simulation while highlighting the critical role of sound mathematical foundations, numerical methodologies, and advanced computational tools in creating data-informed virtual models of physical infrastructures and processes in real time. The discussion includes examples related to smart manufacturing, additive manufacturing technologies, and cyber–physical systems with a focus on the potential for collaboration between physics-informed simulations, data unification, and hybrid machine learning approaches. Central issues including a lack of scalability, measuring uncertainties, interoperability challenges, and ethical concerns are discussed along with rising opportunities for multi/macrodisciplinary research and innovation. This work argues in favor of the continued integration of advanced mathematical approaches with state-of-the-art technologies including artificial intelligence, edge computing, and fifth-generation communication networks with a focus on deploying self-regulating autonomous digital twins. Finally, defeating these challenges via effective collaboration between academia and industry will provide unprecedented society- and economy-wide benefits leading to resilient, optimized, and intelligent systems that mark the future of critical industries and services.