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.
