Calin O. Deep Learning Methods Of Mathematical Physics.Vol I. 2026

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Calin O. Deep Learning Methods Of Mathematical Physics.Vol I. 2026

Textbook in PDF format This book explores how Artificial Intelligence and Deep Learning are transforming Mathematical Physics, offering modern data-driven tools where traditional analytical and numerical methods fall short. As physical systems grow more complex or chaotic, deep learning provides efficient surrogates and physics-informed models capable of capturing dynamics and uncovering governing laws directly from data. This book introduces Neural ODEs, Physics-Informed Neural Networks (PINNs), and Hamiltonian and Lagrangian Neural Networks, showing how they enhance classical mechanics and PDE solvers for both forward and inverse problems. The book is organized into three main parts: The first part is the most elementary and it is an introduction to neural networks and its applications to mathematics problems. The second part focuses on using Deep Learning models to solve forward problems, including classical benchmarks such as the harmonic oscillator, planetary motion, and the simple pendulum. Performance is compared with classical numerical methods. The third part deals with inverse problems, exploring data-driven discovery of system parameters, physical laws, and conservation laws. The book targets senior undergraduates but is also suitable for graduate students, researchers, and practitioners in Physics, Applied Mathematics, Engineering, and Computer Science. The ideal reader is familiar with basic Classical Mechanics, differential equations, and introductory machine learning concepts. Prior experience with Python, TensorFlow, or Keras is helpful but not required; the book provides ample examples and guidance to support implementation