DEEP LEARNING METHODS OF MATHEMATICAL PHYSICS - VOLUME II: HOLONOMIC, NONHOLONOMIC AND STOCHASTIC DYNAMICS

This book explores how Artificial Intelligence and Deep Learning are advancing Mathematical Physics by providing powerful computational tools for systems governed by geometric constraints, stochastic processes, thermodynamics, and complex differential equations. Extending the foundations established in Volume I, it presents modern data-driven and physics-informed approaches for modeling nonlinear dynamics, discovering hidden structures, and solving challenging direct and inverse problems where classical methods become computationally demanding.This book introduces manifold and distribution learning, Physics-Informed Neural Networks (PINNs), variational and structure-preserving neural networks, and thermodynamics-informed models, demonstrating how they preserve geometric and physical principles while solving complex mathematical problems. Covering holonomic and nonholonomic mechanics, Hamiltonian systems, chemical kinetics, generalized solutions of differential equations, and stochastic dynamical systems, it combines mathematical theory with computational experiments, Keras code examples, Google Colab notebooks, and practical exercises. Serving as both an introduction to emerging research directions and a hands-on guide, this book is intended for graduate students, researchers, and practitioners in mathematics, physics, engineering, and computer science seeking advanced applications of Deep Learning in Mathematical Physics.