Hybrid modeling of first-principles and machine learning: A step-by-step tutorial review for practical implementation

In recent years, the integration of mechanistic process models with advanced machine learning techniques has led to the development of hybrid models, which have shown remarkable potential across various domains. However, despite numerous applications and reviews, there is a significant gap in practical resources that guide new researchers through the process of building these models from the ground up. This work addresses this gap by offering a comprehensive tutorial designed to demystify the development of hybrid models. We focus on the practical implementation, beginning with fundamental concepts and advancing to detailed mathematical formulations, providing a step-by-step walkthrough for constructing hybrid models. The tutorial includes detailed case studies illustrating the application of hybrid models in solving complex problems in process systems engineering. By following this guide, researchers will acquire the necessary tools and knowledge to apply hybrid modeling techniques effectively for real-world implementations, paving the way for further innovation and adoption in the field.