دانلود کتاب مدل‌سازی با دانش و داده: مفاهیم و کاربردها برای مهندسان

The material in this book evolved from lectures on Data Driven Modeling and Machine Learning and Dimensional Analysis and Similitude Theory, which I taught over the past decade to aerospace engineering students in the final stages of their master’s studies. Both courses touch on the broader theme of mathematical modeling and emphasize the value of combining physical reasoning with data driven methods to build models that are both practical and meaningful. The interplay between first principles and data gradually emerged as the central thread, and this balance forms the backbone of the present work. Engineering disciplines are traditionally grounded in analytical methods. Curricula emphasize first principles, conservation laws, and mathematical models as the basis for design and analysis. At the same time, engineering practice relies heavily on data from experiments, operational measurements, and numerical simulations. While resources on physical modeling and machine learning are widely available, guidance on integrating these perspectives into coherent models for engineering applications remains rather limited. In my own research and industrial work, particularly in turbomachinery engineering and with industrial data, I have often faced the challenge of developing or applying models that bridge these two worlds, combining first-principle knowledge with data. A system can rarely be described entirely from first principles, and data alone is seldom sufficient to capture the behavior of industrial systems in a meaningful and interpretable way. In practice, hybrid models that combine physics and data often become essential. At the same time, they raise important questions: how much physics should be retained, how should data be integrated, and how can we ensure that the resulting models remain useful, reliable, and generalizable? These questions provided the motivation for this book. The book is intended for graduate students, early stage researchers, and practitioners engaged in the modeling of physical systems, particularly in applied and industrial contexts. The focus lies at the intersection of mathematical modeling in thermo-fluid systems, including fluid mechanics, multiphase _lows, heat transfer, and turbomachinery, and classical machine learning. Rather than serving as a comprehensive reference in any single area, the book offers a practical entry point into combining physical insight with data driven reasoning. The goal is to show how models can be both interpretable and predictive, firmly grounded in physics yet responsive to the realities of imperfect data. At the same time, they should benefit from the generalis ability that physics based reasoning makes possible. The book is organized into three parts. After an introduction to the foundations of modeling, Part I develops the physical background with a focus on thermo-fluid systems, starting from dimensional analysis, progressing through governing equations, simplifications, and canonical cases that often serve as reference solutions. Part II shifts the perspective to uncertainty and data. Here, probability theory, applied statistics, and classical machine learning are presented with an emphasis on the needs of engineers, who often have strong calculus backgrounds but less exposure to statistical reasoning. Part III brings knowledge and data together in practice. It first considers selfcontained processes, where variables and boundary conditions can be well defined, and then addresses complex industrial systems, where operational factors, uneven data, and changing environments introduce additional challenges. Many people have supported me in bringing this book to completion. I am especially grateful to Prof. Dr.-Ing. habil. Bernhard Weigand, who provided me with the opportunity to continue teaching at the University of Stuttgart and to remain engaged with curious and motivated students. His mentorship during my research years and beyond has had a profound impact on my life, and his encouragement greatly supported me in completing this book. I also thank Hannes Mandler, my discussion partner throughout our joint lecture, whose research work provided the basis for the example on eddy viscosity turbulence modeling in the section, and who contributed many valuable comments on the manuscript. My thanks also go to Markus Lempke and Norbert Roth, who have been thoughtful discussion partners over many years, and to Aleksandra Knödelseder, whose careful notes on the chapter were greatly appreciated. I am very grateful for the excellent cooperation with Springer during the preparation of this manuscript. Finally, I owe heartfelt thanks to my family for their patience, understanding, and constant support, which made the completion of this book possible. I hope that readers will find the concepts presented in this book useful, informative, and applicable in their own work. If you wish to share your thoughts, comments, or critiques, I would be glad to hear from you at kdml.gomaa@gmail.com.