Probabilistic Compositional Inference Cuts Power Grid Analysis from Cubic to Linear

In a new paper on arXiv, researchers Esmaeil Ghorbani and Jürgen Hackl propose probabilistic compositional inference (PCI), a graph-based architecture that addresses a critical challenge in engineered infrastructure: inferring hidden states, unknown parameters, and subsystem couplings from sparse, noisy measurements. Traditional approaches require assembling a global augmented state, leading to computational scaling that is cubic in system size—prohibitive for large-scale power grids or multi-physics systems. PCI instead treats each physical subsystem as an independent node with its own local model, estimator, and uncertainty representation, while coupling is handled through physically meaningful stochastic messages exchanged across interfaces. This design allows mechanistic, learned, and deterministic components to coexist, and propagates calibrated uncertainty without ever constructing a global covariance matrix.

The framework was validated in three increasingly demanding settings: a sparse-sensing canonical inverse problem where interface couplings were learned from data; infrastructure-scale power networks where PCI matched centralized joint state-and-parameter inference while reducing computational scaling from approximately cubic to approximately linear; and a multi-physics turbine embedded in a power-grid network, where heterogeneous subsystems composed hierarchically without degrading local inference or collapsing local posteriors. These results demonstrate that subsystem structure itself can serve as the organizing principle for uncertainty-aware inverse inference, offering a practical path to real-time monitoring and control of complex coupled systems without prohibitive computational costs.