A physics-informed SHAP approach for explainable hierarchical planning in gas turbine swarm system

Hierarchical decision-making in dynamic energy systems must balance solution quality with strict online time budgets, especially when high-fidelity nonlinear dynamics are involved. To support fast yet explainable planning and control for gas turbine swarm system, this paper proposes Physics-Informed SHapley Additive explanation (PI-SHAP), an additive attribution metric derived directly from governing differential equations and performance indicators. Unlike conventional SHAP workflows that rely on a separate surrogate or predictive model and incur combinatorial sampling cost, PI-SHAP provides signed, time-resolved contributions of sequential decision variables with substantially reduced computational overhead. To convert these contribution signals into deployable knowledge, we further construct sequential decision trees that map system features to contribution levels and extract interpretable, time-varying rule sets. The resulting rules are compiled into a score-and-rank mechanism for rapid selection among candidate action sequences. The method is validated on a system-level intra-day scheduling problem for a natural-gas pipeline with multiple gas turbine swarms. The evaluation includes numerical reliability checks, rank-based consistency analysis between PI-SHAP scores and true objectives, multi-objective assessment using standard indicators, and impact studies on dataset size and rule granularity. Across these tests, PI-SHAP rules deliver competitive objective values while substantially reducing online decision time compared with optimization-based baselines. We further demonstrate the same rule-extraction pipeline on fast-timescale, controller-in-loop gas-turbine dynamics, where rule evaluation incurs an approximately time-invariant per-step cost and supports rolling decision-making during strongly nonlinear transients. Overall, the results indicate that PI-SHAP coupled with sequential-tree rule compilation, provides an interpretable and computationally efficient decision-support mechanism across slow scheduling and fast control regimes.