Deep Learning Methods of Mathematical Physics: Volume I: Direct and Inverse Problems

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. With Keras code examples, Google Colab notebooks, and practical exercises, this book serves researchers and students in physics, mathematics, and engineering seeking a concise, hands-on guide to applying deep learning in physical systems.

Dr Hans Peter Dietz MD PhD FRANZCOG DDU CU is the world's leading expert on pelvic floorultrasound. He was Professor of Obstetrics and Gynaecology (2008–2021) at University of Sydney, Australiaand co-founded the Australasian Birth Trauma Association in 2017. He has published over 400 peerreviewed papers, with an h-index of 87. He has been a Partner at Sydney Urodynamics for Women since2002 and runs the online Pelvic Floor Imaging course of the International Urogynaecology Association. He isvery active in teaching and has led over 100 courses and seminars worldwide across the last 20 years.