The paper "Learning dynamical systems from data: An introduction to physics-guided deep learning" by Rose Yu and Rui Wang provides an overview of the field of physics-guided deep learning (PGDL), which integrates first-principles physical knowledge into data-driven methods. The authors highlight the challenges and opportunities in modeling complex physical dynamics, emphasizing the need for both computational efficiency and physical realism. They discuss the limitations of traditional physics-based models, such as strong modeling assumptions and high computational costs, and the limitations of deep learning (DL), such as the lack of physical reasoning and interpretability. The paper outlines the learning pipeline for PGDL, including data preparation, model selection, and learning objectives. It categorizes state-of-the-art methods into four groups: residual models, trainable operators, equivariant learning, and disentangled representations, each with increasing dependencies on physical constraints. The authors also address open challenges in the field, such as generalization under distribution shifts, stability and robustness, uncertainty quantification, non-Euclidean geometry, explainability, and causality. Finally, they emphasize the importance of theoretical guarantees to better understand the properties and performance of PGDL models. Overall, the paper serves as a comprehensive introduction to PGDL, highlighting its potential to bridge the gap between physics-based and data-driven approaches in scientific discovery and engineering.The paper "Learning dynamical systems from data: An introduction to physics-guided deep learning" by Rose Yu and Rui Wang provides an overview of the field of physics-guided deep learning (PGDL), which integrates first-principles physical knowledge into data-driven methods. The authors highlight the challenges and opportunities in modeling complex physical dynamics, emphasizing the need for both computational efficiency and physical realism. They discuss the limitations of traditional physics-based models, such as strong modeling assumptions and high computational costs, and the limitations of deep learning (DL), such as the lack of physical reasoning and interpretability. The paper outlines the learning pipeline for PGDL, including data preparation, model selection, and learning objectives. It categorizes state-of-the-art methods into four groups: residual models, trainable operators, equivariant learning, and disentangled representations, each with increasing dependencies on physical constraints. The authors also address open challenges in the field, such as generalization under distribution shifts, stability and robustness, uncertainty quantification, non-Euclidean geometry, explainability, and causality. Finally, they emphasize the importance of theoretical guarantees to better understand the properties and performance of PGDL models. Overall, the paper serves as a comprehensive introduction to PGDL, highlighting its potential to bridge the gap between physics-based and data-driven approaches in scientific discovery and engineering.