Books

This book explores the exciting intersection of machine learning and differential equations (DEs), presenting modern techniques to solve one of the most fundamental mathematical challenges. DEs govern the laws of nature, appearing in contexts as diverse as Einstein's

general relativity, human behavior, and financial markets. Despite their ubiquity, no general analytical method exists to solve them, making

numerical computation the only viable approach.

Over the past decade, advances in neural networks have opened a new approach: Physics-Informed Neural Networks (PINNs). These models transform DEs into trainable neural architectures, enabling solutions with remarkable flexibility and efficiency. Drawing on over ten years of lectures at Harvard University, the authors provide a comprehensive introduction to PINNs, covering the theoretical foundations, algorithmic constructions, and practical techniques needed to implement them.

Readers will gain a thorough understanding of differential equations, numerical methods, neural network architectures, boundary and initial value problems, optimization and sampling methods, and transfer learning strategies. Whether you are a student, researcher, or practitioner, this book equips you with the knowledge and tools to explore and contribute to this rapidly growing field at the cutting edge of science and technology.

A new book compiles my articles on robotization, machine learning, big data and society (now in English). You can get the epub at amazon  ($0.99) here or also can get free versions from this link.

The Covid-19 pandemic has changed much of our vision of the world. It has brought about transformations which demand for new worldviews. This book is a compilation of 40 articles published during the period 2019-21. They are grouped in six thematic sections which have experienced deeps impacts produced by the pandemic in our daily life: (1) Fighting the Maligned Covid-19; (2) Digitalization, Artificial Intelligence, Robotization; (3) Life-styles, Bureaucracy and the Online World; (4) Technological Lords and Industry 4.0; (5) Individual Agency and Social Life; and (6) Recovery and Global Readaptation in a Climate of Uncertainty. The authors have been very keen to ponder how the ongoing robotization is changing our societies, and how our robotized democracies can promote a fairer and equal society. Some particular cases and instances relate to situations in Spain, the EU and the Western Hemisphere. In the main, our analyses cut-cross global areas of examination and inquiry. The overall purpose of this book is to encourage readers to think about life changes and to stimulate their assessment of the processes affecting the pandemic world and the prospects for its indeterminate future.