Partial differntiAl equatioN founDation models and their Application to mobile networks

Objective

The resolution of Partial Differential Equations (PDEs) is fundamental to complex system modelling across a broad range of scientific disciplines, including physics, biology, and engineering. Conventionally, PDEs are solved through numerical methods, which are invariably computationally intensive, thus curbing the adoption of these techniques in intricate problems and real-time applications. Recently, artificial intelligence (AI)-driven approaches have emerged as promising alternatives to approximate with remarkable speed and accuracy, the solution of physics-based PDEs, and ultimately supplant legacy numerical PDE solvers. This action will explore the development of AI-powered frameworks for the resolution of a wide range of physics-based PDEs. These frameworks will be underpinned by universal neural operators that can capture multi-scale and non-linear interactions present in physical phenomena, thereby enabling accurate predictions of physical system behaviour even under dynamic conditions and different families of PDEs. Building on this foundation, the AI-based PDE solvers will be fine-tuned and leveraged to emulate the dynamics of technological non-physical systems. Specifically, they will be employed to forecast the spatiotemporal mobile network traffic demands and user mobility, with the respective traffic demand and mobility PDEs being mined in a data-driven manner. The proposed approach will be validated using real-world data from an operating mobile network, demonstrating the capacity of AI-based PDE solvers to simulate human-made system behaviours. Ultimately, this action will instate the potential of AI in solving both classical physics-based and modern data-driven PDEs, offering a novel perspective on the intersection of physics-driven AI and next-generation digital twin modelling. At the same time, it will mold a multi-dimensional researcher and equip them with skills essential to pivot into the next generation of scientific and academic leaders.