Abstract Machine learning (ML) technique is a critical tool to promote optimal design and ensure reliable and efficient manufacturing in design and manufacturing sector, since it can discover hidden knowledge and build complex relationships by learning patterns from data. However, the inherent `black-box' nature of ML presents a major challenge in interpreting the mechanism and outcomes of the models. Moreover, the reliable predictions of ML highly rely on the amount and quality of training data. To address these issues, physics-informed machine learning (PIML) has emerged as a new research topic. PIML incorporates physical and domain knowledge into ML models to guide the ML training process, which enables more interpretable and reliable models. To fully leverage the advantages of PIML and promote the advancement of design and manufacturing, it is essential for researchers to understand the available PIML methodologies and technical challenges of PIML methods. This paper provides a systematic review of the state-of-the-art in PIML, focusing on the theoretical methods of integrating physics into ML. The PIML techniques are divided into three categories in this paper: hybrid models, physics-loss based models, and physics-embedded architectures. The detailed methodologies are delineated by further stratifying each of these categories according to different integration approaches and ML models. The application cases and physical sources of each technique are also summarized. In addition, the ongoing challenges and potential opportunities of PIML are critically analyzed and discussed, providing a roadmap to narrowing the research gaps in PIML.
Pan et al. (2025) studied this question.