This chapter provides a comprehensive examination of hybrid modeling in chemical and polymer processes, employing a science-guided machine learning (SGML) approach to fuse scientific knowledge with data analytics. We introduce the concept of hybrid SGML and outline our motivation for exploring this innovative approach. A critical review of the broad applications of SGML in chemical engineering highlights the growing complexity and diversity in methodologies, making it challenging for newcomers to navigate the field. To address this, we offer a systematic classification of hybrid SGML methodologies, distinguishing between models where machine learning complements scientific understanding and vice versa. We delve into various applications of machine learning to augment science-based models, discussing direct serial and parallel hybrid modeling, inverse modeling, reduced-order modeling, and the quantification of uncertainty in process models, including the discovery of process governing equations. Each category is explored in detail, evaluating their requirements, strengths, and limitations, and suggesting potential areas of application with specific focus on polyolefin manufacturing. Similarly, we examine how scientific principles can enhance machine learning models, discussing the design, learning, and refinement processes. The study discussing the challenges and opportunities that lie ahead for the hybrid SGML approach in the modeling of chemical and polymer processes, signaling a promising direction for future research and application in this interdisciplinary field. This is a preprint version of our chapter 11 [133] from the book - Integrated Process Modeling, Advanced Control and Data Analytics for Optimizing Polyolefin Manufacturing. Please cite the original work if referenced [144] and is also an extended version of the study [131]. 11.1 Introduction This chapter presents a broad perspective of hybrid modeling combining the scientific knowledge and data analytics in chemical and polymer processes with a science-guided machine learning (SGML) approach. Section 11.1 introduces the hybrid SGML approach and describes our motivation for writing this chapter. Section 11.2 gives a review of the broad applications of hybrid SGML approach in chemical engineering. As the number of reported methodologies and applications continues to rise significantly, it is hard for a person unfamiliar with the subject to identify the appropriate approach for a specific application. This leads to our key focus in Sections 11.3 to 11.5, beginning with a systematic classification and exposition of hybrid SGML methodologies in Section 11.3. We divide the approach into two major categories: ML complements science, and science complements ML. Section 11.4 explains different categories of applying ML to complement science-based models, and presents expositions of direct serial and parallel hybrid modeling and their combinations, inverse modeling, reduced-order modeling, quantifying uncertainty in the process and even discovering governing equations of the process model. We discuss their requirements, strengths and limitations, suggest potential areas of applications, and present illustrative workshops from polyolefin manufacturing. Section 11.5 focuses on different categories of applying scientific principles to complement ML models. We discuss the science- guided design, learning and refinement, together with their requirements, strengths and limitations, as well as their potential applications and application workshops to polyolefin manufacturing. Section 11.6 present a workshop on reduced-order model for a polystyrene process using Aspen Multi-Case and Aspen AI Model Builder. Section 11.7 describes the challenges and opportunities for hybrid SGML approach for modeling chemical and polymer processes. Modeling of many physiochemical systems requires detailed scientific knowledge of the system which is not always feasible for complex processes. We make some assumptions when modeling the system with first principles that ultimately leads to some knowledge gaps in describing the original system. Even for the systems where the scientific knowledge is sufficient to model the system and there is limited data to estimate the multiple parameters of a first-principle model. We often apply data-based models to study the systems where scientific data are available since they are more accurate in prediction. However, data-based/machine learning models are black-box models which can over-fit the data and also produce scientifically inconsistent results. For better accuracy, ML models also require more data which is not always feasible for many problems. Therefore, it is important to integrate science-based knowledge and data-based knowledge for an accurate and scientifically consistent prediction, which we will refer to as hybrid science-guided machine learning (SGML) approach. The most popular hybrid SGML approach that is being practiced in different fields of science is to combine a data-based ML model with a science-based first-principle model. However, there are more ways to combine scientific knowledge and data-based knowledge. In this work, we focus on both aspects of science complementing ML, and ML complementing science. In our development of the hybrid SGML approach, we have benefited from two latest