Physics-informed Machine Learning and Its Research Prospects in GeoAI

Abstract

Scientists still cannot fully understand and explain many complex physical phenomena and dynamic systems, which cannot be described by deterministic mathematic equations and be analyzed and predicted through compact physical mechanistic models. With the ever-increasing of observational data, data-driven machine learning methods can effectively describe many complex non-linear phenomena. Nevertheless, pure data-driven models still have shortcomings in representation, interpretation, generalization capabilities, and sample efficiency. Conventional machine learning methods are confronted with challenges brought by spatiotemporal heterogeneity and sample sparsity. Recently, Physics-Informed Machine Learning (PIML) can effectively leverage observation data to describe and analyze dynamical systems when physical principles are uncertain. PIML has gain wide attention and been extensively applied in physics, computer science, biology, medical science, and geosciences. In recent years, artificial intelligence and machine learning technologies have been widely applied in geography, especially in GIScience and remote sensing, attracting wide research interests of geographers. This line of research is termed GeoAI and has become a cutting-edge research frontier in geography. PIML methods integrate the ideas of model-driven and data-driven methods, introducing new research paradigms for GeoAI and improving the description and prediction of complex geographical phenomena. This survey first summarizes recent progress in this domain from the perspectives of the representation of physical priors and the integration of physical priors in machine learning methods. Physical prior refers to existing independent knowledge that is already available before building machine learning models. This survey reviews the representation of physical priors from the aspects of augmented data and customized features, physical laws and constraints, governing equations as well as geometric properties. We also review how physical priors are integrated into various machine learning models, including constraint modeling, auxiliary task design as well as model training and inference. Based on the PIML survey framework, we explore the relationships between spatiotemporal priors and other physical priors, before briefly reviewing and summarizing typical case studies of spatiotemporal prior-informed GeoAI research. We also discuss the research agenda and future prospects of spatiotemporal prior representation and the spatiotemporal prior-informed GeoAI in the context of geo-machine learning and GeoAI frontiers. In light of fast progress of PIML, we contend that GeoAI studies that are well informed by spatiotemporal priors can gradually establish a generic geographical representation, analysis, prediction, and interpretation framework, which not only helps handle many classical problems in GIScience but also addresses future profound challenges of human being by encouraging geographers to explore more research opportunities when collaborating with researchers from other disciplines.