ICIAM2023 Springer Series – serie

This open access book highlights the critical role of numerical software libraries in advancing applied mathematics and enabling faster, more accurate simulations in science and engineering. These libraries provide high-quality implementations of efficient algorithms, facilitating the transfer of new mathematical methods into practical applications across laboratory and industrial settings. Their importance has grown significantly in recent years, as demonstrated by the U.S. Department of Energy’s Exascale Computing Project (ECP), where libraries have helped applications adapt to cutting-edge exascale systems while improving performance on traditional architectures. The impact of these developments was underscored during the 2023 International Congress on Industrial and Applied Mathematics through a three-part minisymposium titled “Numerical Software Libraries Enabling Benefits to Scientific Applications.” These sessions showcased efforts to maximize the value of libraries, presenting examples of new algorithms and performance enhancements across diverse application areas. This volume compiles chapters based on examples presented during these sessions that illustrate the profound impact of applied mathematics on modern computational science and engineering via modern numerical software libraries.

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.

This book presents a collection of recent advances in stochastic numerical analysis and computational finance. Stochastic numerical methods have played a pivotal role in probability theory, statistics, and applied mathematics, particularly in the rapidly evolving fields of machine learning and data science. They have also achieved significant success in computational finance. The volume highlights cutting-edge developments in numerical techniques for stochastic differential equations and stochastic models in finance. This collection offers valuable insights for researchers and practitioners seeking to deepen their understanding of stochastic modeling and its applications in finance and beyond.

This open access book contains review/research papers authored by fourteen plenary/invited speakers to the 10th International Congress on Industrial and Applied Mathematics (Tokyo, August 20–25, 2023). Written by top-level scientists recognized worldwide, this book covers a wide range topics at the frontline of industrial and applied mathematics. Some of them contain a kind of tutorial, some contain quite readable surveys. We are sure that offering these papers will be a great service to the community of industrial and applied mathematics. This book, which is the Volume 1 of a thematic series dedicated to research results presented at ICIAM 2023, includes also an introductory chapter summarizing the main features of the congress.

This book comes from a mini-symposium held at the ICIAM 2023 congress, coordinated by Giovana Ortigoza Álvarez, a mathematician in Industry (Openpay by BBVA); Ivete Sánchez Bravo, a computational mathematician in Academia focusing on industrial applications (Centro de Investigación en Matemáticas), and Yasmín Á. Ríos Solís, a mathematician in Academia (Tecnologico de Monterrey). The authors then took on the challenge of editing this book. Compiling these success stories was not only intellectually rewarding but also immensely enjoyable. The chapters within this book highlight the diverse applications of applied mathematics, ranging from healthcare and aviation to ecological restoration and logistics. Notable contributions include software solutions for temperature distribution, Bayesian approaches for quality control, and successful industrial problem-solving workshops. This book also covers green logistics, Industry 4.0 developments, and urban transportation planning.

This book is a dedicated collection of invited papers associated with ICIAM 2023. It features twelve contributions covering a broad spectrum of topics in applied and computational mathematics, ranging from mathematical modeling and algorithm development to diverse real-world applications.The contents include research on two-phase flows, fluid-structure interactions, and free boundary and interface problems. Each paper presents advances in mathematical modeling, analytical techniques, and computational methods, reflecting the depth and relevance of current research in these areas. This volume aims to serve as a valuable resource for researchers and practitioners working across disciplines where mathematics plays a central role in understanding and solving complex problems.

This book presents the proceedings of two minisymposia—“Delay and Stochastic Differential Equations in Life Sciences and Engineering” and “Stochastic Modelling in Finance”—held at the International Congress on Industrial and Applied Mathematics (ICIAM) 2023 in Tokyo, Japan. It brings together a diverse collection of theoretical and applied research in delay and stochastic differential equations (DDEs and SDEs), showcasing the depth and breadth of current developments in these areas.The papers included in this book reflect the high quality and versatility of research presented at the sessions. Covering a wide range of topics, they collectively illustrate the richness of delay and stochasticity as drivers of complex dynamical behavior. Each contribution has undergone a rigorous peer-review process to ensure the highest standards of publication.Key topics include delay and resonance, periodic solutions, numerical methods for SDEs, Cesàro limits for Volterra convolution equations, stochastic modeling and big data in finance, incomplete market analysis, deterministic and stochastic pantograph equations. This book aims to provide readers with a cohesive and insightful overview of current research in DDEs and SDEs, while inspiring future innovations and applications across disciplines—from physics and biology to financial engineering.

This book brings together groundbreaking research papers authored by distinguished experts and scholars. Each contribution delves into innovative aspects of splitting optimization—ranging from theoretical advancements and methodological developments to a diverse array of applications. The book offers readers a comprehensive and cohesive overview of the current state of splitting optimization, while inspiring continued research and innovation in this dynamic field.

This book presents a curated collection of recent research contributions in the field of nonlinear partial differential equations (PDEs), with an emphasis on hyperbolic problems. These equations are essential for modeling  complex physical phenomena such as wave propagation, fluid dynamics, blood flow, and sediment transport. In many real-world applications, the governing equations are not purely hyperbolic but involve intricate interactions with elliptic or parabolic components.As the field advances through theoretical insights and practical needs, this volume captures innovative developments shaping current research. The contributions included here were originally presented at the 10th International Congress on Industrial and Applied Mathematics (ICIAM), held in Tokyo in 2023. They were selected from minisymposia on hyperbolic PDEs and related topics, each organized by leading experts in the field.The chapters in this book reflect a rich diversity of perspectives and approaches, ranging from rigorous mathematical analysis to computational techniques and real-world applications. By bringing together these works, the volume offers a comprehensive snapshot of the state of the art in hyperbolic PDE research, highlighting both foundational insights and emerging trends.Edited by the organizers of the relevant ICIAM 2023 minisymposia, this book serves as a valuable resource for researchers, practitioners, and graduate students interested in the theoretical and applied aspects of nonlinear PDEs. Whether you are exploring the mathematical underpinnings of wave phenomena or developing models for complex systems in science and engineering, this volume provides both inspiration and practical tools to advance your work.

This book presents a compelling and up-to-date exploration of modeling techniques for digital twins, a transformative concept revolutionizing how physical assets are designed, operated, optimized, and managed throughout their lifecycle. Digital twins are precise virtual counterparts of physical systems, capable of integrating real-time data to offer dynamic, predictive insights into system behavior. As this paradigm gains momentum across industries, it enhances decision-making and operational efficiency but also introduces new mathematical and engineering challenges in model development.At the core of this volume is a thorough investigation into the modeling frameworks essential for building effective digital twins. These systems must fulfill multifunctional roles, requiring models that are both robust and flexible enough to simulate complex physical processes with high fidelity. The book spans a wide spectrum of approaches from physics-based models grounded in the laws of nature to data-driven techniques that harness large-scale datasets. It also highlights the growing importance of hybrid methods that combine the interpretability of physical models with the adaptability of machine learning. Throughout the book, real-world case studies illustrate how these modeling advancements are applied to solve pressing challenges in sectors such as manufacturing, energy and transportation.This volume brings together contributions from leading researchers who are shaping the future of digital twins. The chapters are designed to be accessible to a broad audience. Whether you just started or want to deepen your expertise, this volume offers the insights and tools needed to engage with one of the most exciting developments in modern applied mathematics and engineering. Chapter 1  is available open access under licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License in  link.springer.com.

This book presents the proceedings of the Minisymposium “Various Methods for the Analysis of PDEs” held at the International Congress on Industrial and Applied Mathematics (ICIAM) 2023. This volume brings together a diverse group of researchers, practitioners, and experts who have shared their latest developments and innovations in the field of Partial Differential Equations (PDEs).The papers included in this volume reflect the high quality and breadth of research presented at the session. Covering a wide range of topics, this collection showcases the dynamic and interdisciplinary nature of the Analysis of PDEs. Each contribution has undergone a rigorous peer-review process to ensure the highest standards of academic excellence.Key topics include:Interpolation Inequalities: Novel contributions to the field, including stability results for the Sobolev inequality and the Gaussian logarithmic Sobolev inequality with explicit and dimensionally sharp constants.Strichartz Estimates: New estimates specifically for orthonormal families of initial data, extending traditional Strichartz estimates to provide deeper insights into the behavior of solutions to dispersive equations, including the wave equation, Klein-Gordon equation, and fractional Schrödinger equations.Asymptotic Behavior: Detailed analysis of the asymptotic behavior for the massive Maxwell–Klein–Gordon system under the Lorenz gauge condition in dimension (1+4), including scattering results.Time-Dependent Free Schrödinger Operator: A new characterization of this operator, highlighting its unique invariance under the Galilei group in Euclidean space-time.Lifespan Estimates: Analysis of the lifespan of solutions to the damped wave equation, with decay estimates for particular initial data in the case of nonlinearity with subcritical Fujita exponent.This book aims to provide readers with a profound and cohesive understanding of the current state of splitting optimization while inspiring future research and innovation in this dynamic field.

This book serves as a primer on a secure computing framework known as federated learning. Federated learning is the study of methods to enable multiple parties to collaboratively train machine learning/AI models, while each party retains its own, raw data on-premise, never sharing it with others. This book is designed to be accessible to anyone with a background in undergraduate applied mathematics. It covers the basics of topics from computer science that are needed to understand examples of simple federated computing frameworks. It is my hope that by learning basic concepts and technical jargon from computer science, readers will be able to start collaborative work with researchers interested in secure computing. Chap. 1 provides the background and motivation for data security and federated learning and the simplest type of neural network. Chap. 2 introduces the idea of multiparty computation (MPC) and why enhancements are needed to provide security and privacy.  Chap. 3 discusses edge computing, a distributed computing model in which data processing takes place on local devices, closer to where it is being generated. Advances in hardware and economies of scale have made it possible for edge computing devices to be embedded in everyday consumer products to process large volumes of data quickly and produce results in near real-time. Chap. 4 covers the basics of federated learning. Federated learning is a framework that enables multiple parties to collaboratively train AI models, while each party retains control of its own raw data, never sharing it with others. Chap. 5 discusses two attacks that target weaknesses of federated learning systems: (1) data leakage, i.e., inferring raw data used to train an AI model by unauthorized parties, and (2) data poisoning, i.e., a cyberattack that compromises data used to train an AI model to manipulate its output.