Mathematics for New Computing Paradigms
Description
The relentless evolution of computing-from classical algorithms to artificial intelligence (AI), brain-inspired architectures, and quantum systems-demands a reimagining of the mathematical foundations that underpin these transformative technologies. Edited by Prof. Shi Jin from Shanghai Jiao Tong University, this volume bridges abstract mathematical theory and cutting-edge computational practice, equipping researchers, engineers, and students with fundamental understanding to navigate and shape the future of scientific computing.
This book unifies interdisciplinary advances in quantum computation, neural and brain-inspired systems, AI-driven molecular modeling, and data-intensive particle dynamics under a cohesive mathematical framework. It synthesizes insights from 9 meticulously structured chapters, each authored by leading experts, to address the mathematical challenges and innovations arising in:
- Quantum advantage for solving partial differential equations (PDEs),
- Biologically plausible AI modeling brain dynamics and protein engineering,
- Statistical rigor in randomized experiments and observational studies,
- Operator learning for kinetic equations and interacting particle systems,
- Graph/hypergraph neural networks via phase-transition physics.
The book aims to reveal the mathematical "language" of next-generation computing paradigms. As computing paradigms fracture into specialized niches, this volume is a unifying compass. It transforms isolated breakthroughs-such as particle-based graph networks, operator learning for chemistry, or quantum PDE solvers-into a coherent mathematical arsenal. For mathematicians, it reveals uncharted problems in computation; for engineers, it provides rigor to harness AI, quantum, and bio-inspired tools; for students, it maps the emerging landscape where equations meet evolution.
More details
Person
Shi Jin is the Director of Institute of Natural Sciences, and Chair Professor of Mathematics, at Shanghai Jiao Tong University. He also serves as a co-director of the Shanghai National Center for Applied Mathematics, director of Ministry of Education Key Lab on Scientific and Engineering Computing, and director of Shanghai Jiao Tong University Chongqing Artificial Intelligence Institute.
He received a Feng Kang Prize of Scientific Computing in 2001., a Morningside Silver Medal in 2007. He is an inaugural Fellow of the American Mathematical Society (AMS) (2012), a Fellow of Society of Industrial and Applied Mathematics (SIAM) (2013), an inaugural Fellow of the Chinese Society of Industrial and Applied Mathematics (CSIAM) (2020), and an Invited Speaker at the International Congress of Mathematicians in 2018. In 2021 he was elected a Foreign Member of Academia Europaea and a Fellow of European Academy of Sciences. In 2024 he was awarded a Shanghai Natural Science Prize (first class).
His research interests include kinetic theory, hyperbolic conservation laws, quantum dynamics, uncertainty quantification, interacting particle systems, computational fluid dynamics, machine learning and quantum computing, etc.
Content
Introduction.- Quantum Computation for Scientific Computing Applications to PDEs.- Modeling Brain Dynamics and Designing Brain Inspired AI Algorithms.- Molecular Dynamics and the Role of Artificial Intelligence.- Generalized AI Solution on Protein Engineering.- Statistical Foundations of Analyzing Randomized Experiments and Observational Studies.- New Computational Methods for Interacting Particle Systems in the Era of Data Science.- Deep Learning for Kinetic Equations.- Allen Cahn Messsage Passing on Graphs and Hypergraphs via Particle System Theory.