Novel Deep Learning Methodologies in Industrial and Applied Mathematics

This book presents a collection of research papers exploring innovative applications of Artificial Intelligence (AI) in Industrial and Applied Mathematics (IAM). It begins with an introduction to the knowlEdge Platform, a software solution for managing the AI lifecycle in Industry 5.0, integrating AI, IoT, and edge computing to support human-AI collaboration across cloud-to-edge systems. The next chapter offers an accessible overview of geometric deep learning, focusing on geometric algebra transformers and their applications. Another contribution discusses eXplainable AI (XAI), highlighting how Clifford geometric algebra can enhance AI interpretability. Further, an improved Quaternion Monogenic Convolutional Neural Network Layer (QMCL) is presented, demonstrating resilience to brightness changes and adversarial attacks. The book also addresses the challenge of balancing computational efficiency, privacy, and accuracy in distributed AI, proposing model partitioning and early exit strategies. A data-driven method for fault prognosis in wind turbine main bearings is introduced, using industrial-scale turbine data. Finally, recent publications—particularly those following the International Congress of Industrial and Applied Mathematics 2023—are reviewed, offering insights into emerging research directions in AI and IAM.