Solving Differential Equations and Inverse Problems with AI: With Problems and Solutions - Part I

Raúl Jiménez, ICREA researcher at the Institute of Cosmos Sciences of the University of Barcelona (ICCUB), has published a new book on the exciting intersection between artificial intelligence and differential equations, Solving Differential Equations and Inverse Problems with AI: With Problems and Solutions - Part I, co-authored with Pavlos Protopapas of Harvard University. 

The book introduces readers to modern AI-based methods for solving differential equations and inverse problems, two mathematical tools that play a central role across many scientific disciplines, especially in Physics. Differential equations govern the laws of nature, appearing in contexts as diverse as Einstein's general relativity, human behavior, and financial market. Yet many of these equations cannot be solved exactly, making numerical and computational approaches essential. 
A key focus of the book is on Physics-Informed Neural Networks (PINNs), a rapidly developing family of machine learning techniques that incorporate physical laws directly into neural network models. By combining artificial intelligence with established mathematical principles, these methods offer new ways of tackling complex scientific problems. 

Unlike many introductory AI texts, the authors place a strong emphasis on the underlying mathematics. The volume includes worked examples, exercises and detailed solutions, aiming to provide readers with both a conceptual and practical understanding of the subject. Drawing on more than a decade of teaching experience, Jiménez and Protopapas guide readers through differential equations, numerical methods, neural network architectures, optimisation techniques and transfer learning strategies. 
The publication reflects a growing trend in contemporary science: the integration of AI techniques into fundamental research. From cosmology and particle physics to engineering and the life sciences, machine learning is opening new possibilities for analysing data, modelling systems and solving previously intractable problems.

The title's reference to "Part I" is intentional. The authors are already working on a second volume that will continue exploring advanced applications and methods at the frontier of AI-driven scientific computing.

Solving Differential Equations and Inverse Problems with AI: With Problems and Solutions - Part I is available through World Scientific Publishing. 

Reference
Protopapas, P. & Jiménez, R. (2026). Solving Differential Equations and Inverse Problems with AI: With Problems and Solutions - Part I. World Scientific Publishing.