Physics-Guided Machine Learning for Carbon Emission Modeling under System Disruptions: Methods and Challenges

Disruptions such as pandemics and energy shocks weaken the reliability of carbon-emission models. Physics-guided machine learning (PIML) offers a practical response. This review explains how PIML improves robustness when temporal continuity breaks and system structure shifts. It covers four methods: physics-informed neural networks; hybrid or embedded designs that use CTM outputs and differentiable operators; post-processing that enforces physical feasibility; and structured or graph-based models that encode conservation and transport while keeping interpretability. Evidence shows these methods are more robust with sparse data and under distribution shifts. Yet challenges remain: balancing loss terms, dealing with complex boundaries, keeping physical inputs up to date, and the high cost of multi-scale problems. On the application side, the review focuses on pandemic-driven demand contraction, energy-supply shocks with fuel switching, and policy-induced structural change. These scenarios guide evaluation and benchmarks and help improve reliability under disruptions. On the practice side, recommended tactics include reliability-weighted fusion, adaptive coupling, explicit uncertainty handling, and dynamic graphs.