Computational Differential Equations with AI: Modern Machine Learning Approaches
Hardcover
Series: Synthesis Lectures on Mathematics & Statistics
General MathematicsProbability & Statistics
ISBN13: 9783032225733
Publisher: Springer
Published: Oct 28 2026
Pages: 132
Language: English
This book provides cutting-edge machine learning (ML) methods, including Physics-Informed Neural Networks (PINNs), Neural Operators, and other ML methods, for solving ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic systems. Differential equations (DEs) are the basic foundation for modeling real-world problems in various fields such as physics, engineering, finance, and biology. Solving DEs requires complicated mathematical methods; however, ML is now a viable, innovative, and alternative technique. This book aims to bridge the gap between DEs and ML by explaining how to utilize neural networks, physics-informed models, and other artificial intelligence (AI) based techniques to solve DEs more efficiently and accurately. With the use of ML techniques, readers can also uncover hidden patterns within the data of the problem.The authors utilize Python throughout to implement and demonstrate the methods behind the various presented examples. This book is an ideal choice for academic researchers, engineers, data scientists, and others who are interested in ML methods and real-world applications to democratize next-generational computational mathematics.
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