Towards General Equations of Science From Dimensional Analysis to Functional Networks and Probabilistic Models

This open access book offers a bold and unifying vision of how scientific knowledge can be expressed through universal mathematical structures. Moving from classical dimensional analysis to modern probabilistic and data-driven frameworks, this book reveals deep connections between seemingly disparate fields.

Beginning with the foundations of the Buckingham Pi theorem, the authors guide the reader toward a broader perspective where functional equations, copulas, Bayesian networks, and functional networks emerge as parts of a single coherent framework. The work introduces powerful tools for modeling complex systems, emphasizing how relationships between variables can be captured, generalized, and extended across disciplines.

Bridging theory and application, the book explores engineering, physics, and data science problems while introducing innovative concepts such as opacity technique to reveal conditional-density structures in data clouds, conditional modeling with events of positive probability, and new approaches to artificial intelligence grounded in structure rather than blackbox methods.

Designed for researchers, engineers, and advanced students, this book is both a reference and a source of new ideas. It challenges conventional modeling approaches and invites readers to rethink how scientific laws are discovered, represented, and applied in an increasingly data-rich world.