Modern physical systems are experiencing tremendous evolutions with growing size, more and more complex structures, and the incorporation of new devices. This calls for better planning, monitoring, and control. However, achieving these goals is challenging since the system knowledge (e.g., system structures and edge parameters) may be unavailable for a normal system, let alone some dynamic changes like maintenance, reconfigurations, and events, etc. Therefore, extracting system knowledge becomes a central topic. Luckily, advanced metering techniques bring numerous data, leading to the emergence of Machine Learning (ML) methods with efficient learning and fast inference. This work tries to propose a systematic framework of ML-based methods to learn system knowledge under three what-if scenarios: (i) What if the system is normally operated? (ii) What if the system suffers dynamic interventions? (iii) What if the system is new with limited data? For each case, this thesis proposes principled solutions with extensive experiments. Chapter 2 tackles scenario (i) and the golden rule is to learn an ML model that maintains physical consistency, bringing high extrapolation capacity for changing operational conditions. The key finding is that physical consistency can be linked to convexity, a central concept in optimization. Therefore, convexified ML designs are proposed and the global optimality implies faithfulness to the underlying physics. Chapter 3 handles scenario (ii) and the goal is to identify the event time, type, and locations. The problem is formalized as multi-class classification with special attention to accuracy and speed. Subsequently, Chapter 3 builds an ensemble learning framework to aggregate different ML models for better prediction. Next, to tackle high-volume data quickly, a tensor as the multi-dimensional array is used to store and process data, yielding compact and informative vectors for fast inference. Finally, if no labels exist, Chapter 3 uses physical properties to generate labels for learning. Chapter 4 deals with scenario (iii) and a doable process is to transfer knowledge from similar systems, under the framework of Transfer Learning (TL). Chapter 4 proposes cutting-edge system-level TL by considering the network structure, complex spatial-temporal correlations, and different physical information.