A New Unified Methodology for Physics and Data Hybrid Modeling—Showcase in Maritime

Abstract

Hybrid modeling, which integrates physics-based knowledge with data-driven learning, has emerged as a promising paradigm for complex industrial cyber-physical systems where neither approach alone is sufficient. However, most existing works focus on exploring new hybrid algorithms for specific tasks, while limited attention has been given to systematic guidance for hybrid model design across heterogeneous applications. This paper introduces a unified hybrid modeling methodology that characterizes hybrid systems along two fundamental dimensions: the functional modes (complementary, cooperative, and competitive) and the canonical topologies (sequential, parallel, and embedded). This formulation enables systematic reasoning about how physics and data should interact under different knowledge–data conditions. The methodology is domain-agnostic and applicable to a wide range of industrial cyber-physical systems. Maritime applications are used in this study as a stress-test domain due to their safety-critical nature, complex environmental interactions, and limited availability of large datasets. Four representative case studies, including motion control, dynamics identification, fuel consumption estimation, and sea-state prediction, demonstrate how different hybrid configurations emerge naturally under varying knowledge and data availability. The results show that the proposed framework provides practical guidance for selecting appropriate hybrid modeling strategies in real-world engineering applications.