  Recent advances of data-driven machine learning have revolutionized fields
like computer vision, reinforcement learning, and many scientific and
engineering domains. In many real-world and scientific problems, systems that
generate data are governed by physical laws. Recent work shows that it provides
potential benefits for machine learning models by incorporating the physical
prior and collected data, which makes the intersection of machine learning and
physics become a prevailing paradigm. By integrating the data and mathematical
physics models seamlessly, it can guide the machine learning model towards
solutions that are physically plausible, improving accuracy and efficiency even
in uncertain and high-dimensional contexts. In this survey, we present this
learning paradigm called Physics-Informed Machine Learning (PIML) which is to
build a model that leverages empirical data and available physical prior
knowledge to improve performance on a set of tasks that involve a physical
mechanism. We systematically review the recent development of physics-informed
machine learning from three perspectives of machine learning tasks,
representation of physical prior, and methods for incorporating physical prior.
We also propose several important open research problems based on the current
trends in the field. We argue that encoding different forms of physical prior
into model architectures, optimizers, inference algorithms, and significant
domain-specific applications like inverse engineering design and robotic
control is far from being fully explored in the field of physics-informed
machine learning. We believe that the interdisciplinary research of
physics-informed machine learning will significantly propel research progress,
foster the creation of more effective machine learning models, and also offer
invaluable assistance in addressing long-standing problems in related
disciplines.
