Learning with Support Vector Machines

From Equations to Applications
Erscheinungsjahr 2026
ISBN: 978-3-032-33734-4
Verlag: Springer

Buch, Englisch, 143 Seiten, Format (B × H): 168 mm x 240 mm

Reihe: Synthesis Lectures on Mathematics & Statistics

This book focuses on Support Vector Machine (SVM), Least Square SVM (LS-SVM), and Physics-Informed LS-SVM (PILSSVM) and bridges the gap among mathematical theory, physical modeling, and practical machine learning. The authors focus on method-driven, kernel-based learning to solve ordinary differential equations (ODEs) and partial differential equations (PDEs), which is most relevant in real-world scientific and engineering domains. The book introduces core concepts through a problem-solving lens and provides a unified, structured, and progressive exposition starting from fundamentals to advanced methods. Machine learning is changing how problems are solved in science, engineering, and daily life, from diagnosing diseases to predicting market trends. One of the most effective and widely used tools in this field is SVM, and this book explains how SVM and their advanced forms work, not just in theory, but also in solving differential equations across science and engineering. In addition, the authors discuss how mathematical equations connect with practical needs, such as modeling natural disasters, analyzing financial trends, or simulating engineering systems, all using intelligent data driven methods. There is a growing demand for accessible, structured learning material that helps domain experts apply SVM-based techniques effectively, and this book fills that gap by providing both the logic behind the method and hands on examples that show how to use it. With the solution of different types of differential equations, the authors equip researchers, practitioners, and students with the tools needed to apply kernel-based machine learning methods to equations, experiments, and emerging challenges in data-driven modeling.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Chakraverty, Snehashish

Mishra, Bhubaneswari

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

From Classical Solvers to Kernel Intelligence.- Solving Ordinary Differential Equations Using LSSVM.- Tackling Partial Differential Equations with LSSVM.- Physics-Informed LSSVM for Smarter ODE Solutions.- Solving PDEs with Physics at the Core.- Modeling Financial Markets with PILSSVM.- Simulating Fluid Flows Using Physics-Informed Kernels.

Über Autor(innen)

Snehashish Chakraverty, Ph.D., is a Professor in the Department of Mathematics at the National Institute of Technology Rourkela, India.  He is a globally recognized academician and researcher with over 30 years of experience in the fields of mathematical modeling, structural mechanics, uncertainty quantification, and computational methods. Dr. Chakraverty has authored more than 35 books and 340 peer-reviewed journal articles published by reputed publishers. He has also served as the editor and editorial board member of numerous international journals and has received numerous national and international awards for his contributions to mathematical modeling and applied mechanics. His recent research spans soft computing, AI techniques in mechanics, and computational modeling of smart structures.

Bhubaneswari Mishra is a Senior Research Fellow in the Department of Mathematics at the National Institute of Technology Rourkela, India, with a specialization in artificial intelligence and applied mathematics. Her research focuses on developing kernel-based and physics-informed machine learning methods, such as LS-SVM and PILSSVM, to solve complex differential equations arising in financial modeling, geophysical systems, and biomedical applications. She holds a Master’s degree in Mathematics and Computing and has published multiple research papers, book chapters, and peer-reviewed conference papers. She has actively presented her research at several national and international conferences and workshops. In addition to academic work, she has been collaborating with CRISIL Ltd. for over four years as part of an industry-academia research program focused on AI-driven financial risk modeling.