Neural Operators with Python Code

This book provides a practical introduction to Neural Operators, with a particular focus on Fourier Neural Operators (FNOs) and their applications to solid dynamics.

Neural Operators offer a fundamentally different approach to scientific computing by learning mappings directly between input functions and solution functions. Once trained, they can predict solutions for previously unseen input functions and physical parameters in near real time, without requiring a new, computationally expensive numerical simulation for each prediction.

The book develops these concepts through progressively more sophisticated case studies in the elastodynamics of one-, two-, and three-dimensional solids. The examples cover a range of physical scenarios, including initial displacement fields, time-dependent external forces, varying wave speeds, and different material properties.

A defining feature of this book is its code-driven approach. Complete, self-contained Python implementations are provided for finite element method solvers for high-fidelity dataset generation, FNO model construction, training, and evaluation. The mathematical foundations and formulations are presented alongside executable Python packages and JupyterLab notebooks, enabling readers to move seamlessly from theory to implementation.

Designed for students, researchers, and practicing engineers, this book combines a solid theoretical foundation in Neural Operators with practical computational tools for applying them to physical systems governed by partial differential equations (PDEs).

Learn the theory. Run the code. Explore Neural Operators.