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Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, PIML models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, PIML models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of PIML is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in PIML for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of PIML models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.
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This content will become publicly available on June 1, 2026
When physics meets machine learning: a survey of physics-informed machine learning
Abstract Physics-informed machine learning (PIML), the combination of prior physics knowledge with data-driven machine learning models, has emerged as an effective means of mitigating a shortage of training data, increasing model generalizability, and ensuring physical plausibility of results. In this paper, we survey a wide variety of recent works in PIML and summarize them from three key aspects: 1) motivations of PIML, 2) physics knowledge in PIML, and 3) methods of physics knowledge integration in PIML. We additionally discuss current challenges and corresponding research opportunities in PIML.
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- Award ID(s):
- 2425919
- PAR ID:
- 10632099
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Machine Learning for Computational Science and Engineering
- Volume:
- 1
- Issue:
- 1
- ISSN:
- 3005-1428
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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