Multi-Domain Graph-Based Modeling of Energy Systems with Applications to Lithium-Ion Batteries

What the math gives to ML

The paper contributes two constructive graph-modeling mechanisms: recursive state-to-input feedback for representing non-adjacent dependencies without adding graph edges, and parallel decomposition of a composite edge into single-input edges while preserving vertex-level power conservation. These mechanisms transfer naturally to graph neural networks by separating topology from learned long-range feedback and by enforcing conservation through signed incidence aggregation. The strongest neural-network use is in physical or relational forecasting, where the constructions predict measurable reductions in conservation residuals and long-horizon rollout drift rather than relying only on benchmark accuracy.